LMFDB - Embedded newform 225.2.e.b.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(76,225)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$1.71903 + 0.211943i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.2.e.b.76.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04307 + 1.80664i) q^{2} +(1.04307 - 1.38276i) q^{3} +(-1.17597 - 2.03684i) q^{4} +(1.41016 + 3.32675i) q^{6} +(2.04307 - 3.53869i) q^{7} +0.734191 q^{8} +(-0.824030 - 2.88461i) q^{9} +O(q^{10})$	\(q+(-1.04307 + 1.80664i) q^{2} +(1.04307 - 1.38276i) q^{3} +(-1.17597 - 2.03684i) q^{4} +(1.41016 + 3.32675i) q^{6} +(2.04307 - 3.53869i) q^{7} +0.734191 q^{8} +(-0.824030 - 2.88461i) q^{9} +(0.675970 - 1.17081i) q^{11} +(-4.04307 - 0.498476i) q^{12} +(0.324030 + 0.561237i) q^{13} +(4.26210 + 7.38217i) q^{14} +(1.58613 - 2.74726i) q^{16} +1.35194 q^{17} +(6.07097 + 1.52011i) q^{18} +0.648061 q^{19} +(-2.76210 - 6.51615i) q^{21} +(1.41016 + 2.44247i) q^{22} +(2.39500 + 4.14827i) q^{23} +(0.765809 - 1.01521i) q^{24} -1.35194 q^{26} +(-4.84823 - 1.86940i) q^{27} -9.61033 q^{28} +(-1.93807 + 3.35683i) q^{29} +(3.84823 + 6.66533i) q^{31} +(4.04307 + 7.00279i) q^{32} +(-0.913870 - 2.15594i) q^{33} +(-1.41016 + 2.44247i) q^{34} +(-4.90645 + 5.07063i) q^{36} -7.52420 q^{37} +(-0.675970 + 1.17081i) q^{38} +(1.11404 + 0.137352i) q^{39} +(0.0898394 + 0.155606i) q^{41} +(14.6534 + 1.80664i) q^{42} +(-0.410161 + 0.710419i) q^{43} -3.17968 q^{44} -9.99258 q^{46} +(5.45323 - 9.44526i) q^{47} +(-2.14435 - 5.05880i) q^{48} +(-4.84823 - 8.39738i) q^{49} +(1.41016 - 1.86940i) q^{51} +(0.762100 - 1.32000i) q^{52} -4.17226 q^{53} +(8.43436 - 6.80911i) q^{54} +(1.50000 - 2.59808i) q^{56} +(0.675970 - 0.896110i) q^{57} +(-4.04307 - 7.00279i) q^{58} +(-2.08613 - 3.61328i) q^{59} +(1.91016 - 3.30850i) q^{61} -16.0558 q^{62} +(-11.8913 - 2.97746i) q^{63} -10.5242 q^{64} +(4.84823 + 0.597746i) q^{66} +(4.07097 + 7.05113i) q^{67} +(-1.58984 - 2.75368i) q^{68} +(8.23419 + 1.01521i) q^{69} -6.11644 q^{71} +(-0.604996 - 2.11785i) q^{72} +12.3445 q^{73} +(7.84823 - 13.5935i) q^{74} +(-0.762100 - 1.32000i) q^{76} +(-2.76210 - 4.78410i) q^{77} +(-1.41016 + 1.86940i) q^{78} +(-5.17226 + 8.95862i) q^{79} +(-7.64195 + 4.75401i) q^{81} -0.374833 q^{82} +(-6.12920 + 10.6161i) q^{83} +(-10.0242 + 13.2887i) q^{84} +(-0.855648 - 1.48203i) q^{86} +(2.62015 + 6.18127i) q^{87} +(0.496291 - 0.859601i) q^{88} -3.00000 q^{89} +2.64806 q^{91} +(5.63290 - 9.75648i) q^{92} +(13.2305 + 1.63121i) q^{93} +(11.3761 + 19.7041i) q^{94} +(13.9003 + 1.71380i) q^{96} +(-6.79001 + 11.7606i) q^{97} +20.2281 q^{98} +(-3.93436 - 0.985122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9}+O(q^{10}) $ 6 * q + q^2 - q^3 - 5 * q^4 - 4 * q^6 + 5 * q^7 - 6 * q^8 - 7 * q^9	$ 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9} + 2 q^{11} - 17 q^{12} + 4 q^{13} + 9 q^{14} - 5 q^{16} + 4 q^{17} + 23 q^{18} + 8 q^{19} - 4 q^{22} + 3 q^{23} + 15 q^{24} - 4 q^{26} + 2 q^{27} - 10 q^{28} + 7 q^{29} - 8 q^{31} + 17 q^{32} - 20 q^{33} + 4 q^{34} + 10 q^{36} - 12 q^{37} - 2 q^{38} - 14 q^{39} + 13 q^{41} + 33 q^{42} + 10 q^{43} - 44 q^{44} - 6 q^{46} + 13 q^{47} + 10 q^{48} + 2 q^{49} - 4 q^{51} - 12 q^{52} + 4 q^{53} + 5 q^{54} + 9 q^{56} + 2 q^{57} - 17 q^{58} + 2 q^{59} - q^{61} - 84 q^{62} - 33 q^{63} - 30 q^{64} - 2 q^{66} + 11 q^{67} - 22 q^{68} + 39 q^{69} - 20 q^{71} - 15 q^{72} + 16 q^{73} + 16 q^{74} + 12 q^{76} + 4 q^{78} - 2 q^{79} - 19 q^{81} + 58 q^{82} - 15 q^{83} - 27 q^{84} - 28 q^{86} + 26 q^{87} - 24 q^{88} - 18 q^{89} + 20 q^{91} + 39 q^{92} + 42 q^{93} + 31 q^{94} + 13 q^{96} - 18 q^{97} + 80 q^{98} + 22 q^{99}+O(q^{100}) $ 6 * q + q^2 - q^3 - 5 * q^4 - 4 * q^6 + 5 * q^7 - 6 * q^8 - 7 * q^9 + 2 * q^11 - 17 * q^12 + 4 * q^13 + 9 * q^14 - 5 * q^16 + 4 * q^17 + 23 * q^18 + 8 * q^19 - 4 * q^22 + 3 * q^23 + 15 * q^24 - 4 * q^26 + 2 * q^27 - 10 * q^28 + 7 * q^29 - 8 * q^31 + 17 * q^32 - 20 * q^33 + 4 * q^34 + 10 * q^36 - 12 * q^37 - 2 * q^38 - 14 * q^39 + 13 * q^41 + 33 * q^42 + 10 * q^43 - 44 * q^44 - 6 * q^46 + 13 * q^47 + 10 * q^48 + 2 * q^49 - 4 * q^51 - 12 * q^52 + 4 * q^53 + 5 * q^54 + 9 * q^56 + 2 * q^57 - 17 * q^58 + 2 * q^59 - q^61 - 84 * q^62 - 33 * q^63 - 30 * q^64 - 2 * q^66 + 11 * q^67 - 22 * q^68 + 39 * q^69 - 20 * q^71 - 15 * q^72 + 16 * q^73 + 16 * q^74 + 12 * q^76 + 4 * q^78 - 2 * q^79 - 19 * q^81 + 58 * q^82 - 15 * q^83 - 27 * q^84 - 28 * q^86 + 26 * q^87 - 24 * q^88 - 18 * q^89 + 20 * q^91 + 39 * q^92 + 42 * q^93 + 31 * q^94 + 13 * q^96 - 18 * q^97 + 80 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.04307	+	1.80664i	−0.737558	+	1.27749i	0.216033	+	0.976386i	$0.430688\pi$
$2$	−1.04307	+	1.80664i	−0.737558	+	1.27749i	−0.953592	+	0.301103i	$0.902645\pi$
$3$	1.04307	−	1.38276i	0.602214	−	0.798335i
$3$	1.04307	−	1.38276i	0.602214	−	0.798335i
$4$	−1.17597	−	2.03684i	−0.587985	−	1.01842i
$5$		0			0
$5$		0			0
$6$	1.41016	+	3.32675i	0.575696	+	1.35814i
$7$	2.04307	−	3.53869i	0.772206	−	1.33750i	−0.164145	−	0.986436i	$-0.552487\pi$
$7$	2.04307	−	3.53869i	0.772206	−	1.33750i	0.936351	−	0.351064i	$-0.114180\pi$
$8$	0.734191			0.259576
$9$	−0.824030	−	2.88461i	−0.274677	−	0.961537i
$10$		0			0
$11$	0.675970	−	1.17081i	0.203813	−	0.353014i	−0.745941	−	0.666012i	$-0.768000\pi$
$11$	0.675970	−	1.17081i	0.203813	−	0.353014i	0.949754	+	0.312998i	$0.101333\pi$
$12$	−4.04307	−	0.498476i	−1.16713	−	0.143898i
$13$	0.324030	+	0.561237i	0.0898699	+	0.155659i	0.907456	−	0.420147i	$-0.138022\pi$
$13$	0.324030	+	0.561237i	0.0898699	+	0.155659i	−0.817586	+	0.575806i	$0.804688\pi$
$14$	4.26210	+	7.38217i	1.13909	+	1.97297i
$15$		0			0
$16$	1.58613	−	2.74726i	0.396533	−	0.686815i
$17$	1.35194			0.327893			0.163947	−	0.986469i	$-0.447577\pi$
$17$	1.35194			0.327893			0.163947	+	0.986469i	$0.447577\pi$
$18$	6.07097	+	1.52011i	1.43094	+	0.358293i
$19$	0.648061			0.148675			0.0743377	−	0.997233i	$-0.476316\pi$
$19$	0.648061			0.148675			0.0743377	+	0.997233i	$0.476316\pi$
$20$		0			0
$21$	−2.76210	−	6.51615i	−0.602740	−	1.42194i
$22$	1.41016	+	2.44247i	0.300647	+	0.520736i
$23$	2.39500	+	4.14827i	0.499393	+	0.864974i	1.00000		0.000700856i	$-0.000223089\pi$
$23$	2.39500	+	4.14827i	0.499393	+	0.864974i	−0.500607	+	0.865675i	$0.666890\pi$
$24$	0.765809	−	1.01521i	0.156320	−	0.207228i
$25$		0			0
$26$	−1.35194			−0.265137
$27$	−4.84823	−	1.86940i	−0.933042	−	0.359767i
$28$	−9.61033			−1.81618
$29$	−1.93807	+	3.35683i	−0.359890	+	0.623349i	−0.987942	−	0.154823i	$-0.950519\pi$
$29$	−1.93807	+	3.35683i	−0.359890	+	0.623349i	0.628052	+	0.778172i	$0.283853\pi$
$30$		0			0
$31$	3.84823	+	6.66533i	0.691163	+	1.19713i	0.971457	+	0.237215i	$0.0762345\pi$
$31$	3.84823	+	6.66533i	0.691163	+	1.19713i	−0.280295	+	0.959914i	$0.590432\pi$
$32$	4.04307	+	7.00279i	0.714720	+	1.23793i
$33$	−0.913870	−	2.15594i	−0.159084	−	0.375300i
$34$	−1.41016	+	2.44247i	−0.241841	+	0.418880i
$35$		0			0
$36$	−4.90645	+	5.07063i	−0.817742	+	0.845105i
$37$	−7.52420			−1.23697			−0.618485	−	0.785796i	$-0.712253\pi$
$37$	−7.52420			−1.23697			−0.618485	+	0.785796i	$0.712253\pi$
$38$	−0.675970	+	1.17081i	−0.109657	+	0.189931i
$39$	1.11404	+	0.137352i	0.178389	+	0.0219939i
$40$		0			0
$41$	0.0898394	+	0.155606i	0.0140306	+	0.0243016i	0.872955	−	0.487800i	$-0.162200\pi$
$41$	0.0898394	+	0.155606i	0.0140306	+	0.0243016i	−0.858925	+	0.512102i	$0.828867\pi$
$42$	14.6534	+	1.80664i	2.26107	+	0.278771i
$43$	−0.410161	+	0.710419i	−0.0625489	+	0.108338i	−0.895604	−	0.444852i	$-0.853256\pi$
$43$	−0.410161	+	0.710419i	−0.0625489	+	0.108338i	0.833055	+	0.553190i	$0.186590\pi$
$44$	−3.17968			−0.479355
$45$		0			0
$46$	−9.99258			−1.47333
$47$	5.45323	−	9.44526i	0.795435	−	1.37773i	−0.127128	−	0.991886i	$-0.540576\pi$
$47$	5.45323	−	9.44526i	0.795435	−	1.37773i	0.922563	−	0.385847i	$-0.126091\pi$
$48$	−2.14435	−	5.05880i	−0.309510	−	0.730175i
$49$	−4.84823	−	8.39738i	−0.692604	−	1.19963i
$50$		0			0
$51$	1.41016	−	1.86940i	0.197462	−	0.261769i
$52$	0.762100	−	1.32000i	0.105684	−	0.183050i
$53$	−4.17226			−0.573104			−0.286552	−	0.958065i	$-0.592509\pi$
$53$	−4.17226			−0.573104			−0.286552	+	0.958065i	$0.592509\pi$
$54$	8.43436	−	6.80911i	1.14777	−	0.926602i
$55$		0			0
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	0.675970	−	0.896110i	0.0895344	−	0.118693i
$58$	−4.04307	−	7.00279i	−0.530880	−	0.919512i
$59$	−2.08613	−	3.61328i	−0.271591	−	0.470409i	0.697678	−	0.716411i	$-0.254216\pi$
$59$	−2.08613	−	3.61328i	−0.271591	−	0.470409i	−0.969269	+	0.246002i	$0.920883\pi$
$60$		0			0
$61$	1.91016	−	3.30850i	0.244571	−	0.423609i	−0.717440	−	0.696620i	$-0.754686\pi$
$61$	1.91016	−	3.30850i	0.244571	−	0.423609i	0.962011	+	0.273011i	$0.0880195\pi$
$62$	−16.0558			−2.03909
$63$	−11.8913	−	2.97746i	−1.49816	−	0.375124i
$64$	−10.5242			−1.31552
$65$		0			0
$66$	4.84823	+	0.597746i	0.596776	+	0.0735775i
$67$	4.07097	+	7.05113i	0.497349	+	0.861433i	0.999995	−	0.00305885i	$-0.000973664\pi$
$67$	4.07097	+	7.05113i	0.497349	+	0.861433i	−0.502647	+	0.864492i	$0.667640\pi$
$68$	−1.58984	−	2.75368i	−0.192796	−	0.333933i
$69$	8.23419	+	1.01521i	0.991280	+	0.122217i
$70$		0			0
$71$	−6.11644			−0.725888			−0.362944	−	0.931811i	$-0.618228\pi$
$71$	−6.11644			−0.725888			−0.362944	+	0.931811i	$0.618228\pi$
$72$	−0.604996	−	2.11785i	−0.0712994	−	0.249592i
$73$	12.3445			1.44482			0.722408	−	0.691467i	$-0.243035\pi$
$73$	12.3445			1.44482			0.722408	+	0.691467i	$0.243035\pi$
$74$	7.84823	−	13.5935i	0.912338	−	1.58022i
$75$		0			0
$76$	−0.762100	−	1.32000i	−0.0874188	−	0.151414i
$77$	−2.76210	−	4.78410i	−0.314770	−	0.545198i
$78$	−1.41016	+	1.86940i	−0.159669	+	0.211668i
$79$	−5.17226	+	8.95862i	−0.581925	+	1.00792i	0.413326	+	0.910583i	$0.364367\pi$
$79$	−5.17226	+	8.95862i	−0.581925	+	1.00792i	−0.995251	+	0.0973403i	$0.968966\pi$
$80$		0			0
$81$	−7.64195	+	4.75401i	−0.849105	+	0.528224i
$82$	−0.374833			−0.0413934
$83$	−6.12920	+	10.6161i	−0.672767	+	1.16527i	0.304350	+	0.952560i	$0.401561\pi$
$83$	−6.12920	+	10.6161i	−0.672767	+	1.16527i	−0.977116	+	0.212706i	$0.931772\pi$
$84$	−10.0242	+	13.2887i	−1.09373	+	1.44992i
$85$		0			0
$86$	−0.855648	−	1.48203i	−0.0922669	−	0.159811i
$87$	2.62015	+	6.18127i	0.280910	+	0.662702i
$88$	0.496291	−	0.859601i	0.0529048	−	0.0916338i
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	2.64806			0.277592
$92$	5.63290	−	9.75648i	0.587271	−	1.01718i
$93$	13.2305	+	1.63121i	1.37194	+	0.169148i
$94$	11.3761	+	19.7041i	1.17336	+	2.03232i
$95$		0			0
$96$	13.9003	+	1.71380i	1.41870	+	0.174914i
$97$	−6.79001	+	11.7606i	−0.689421	+	1.19411i	0.282605	+	0.959237i	$0.408802\pi$
$97$	−6.79001	+	11.7606i	−0.689421	+	1.19411i	−0.972025	+	0.234876i	$0.924532\pi$
$98$	20.2281			2.04334
$99$	−3.93436	−	0.985122i	−0.395418	−	0.0990085i
$100$		0			0
$101$	0.734191	−	1.27166i	0.0730547	−	0.126535i	−0.827184	−	0.561931i	$-0.810059\pi$
$101$	0.734191	−	1.27166i	0.0730547	−	0.126535i	0.900239	+	0.435397i	$0.143392\pi$
$102$	1.90645	+	4.49756i	0.188767	+	0.445325i
$103$	3.76210	+	6.51615i	0.370691	+	0.642055i	0.989672	−	0.143351i	$-0.0457877\pi$
$103$	3.76210	+	6.51615i	0.370691	+	0.642055i	−0.618981	+	0.785406i	$0.712454\pi$
$104$	0.237900	+	0.412055i	0.0233280	+	0.0404053i
$105$		0			0
$106$	4.35194	−	7.53778i	0.422698	−	0.732134i
$107$	−1.20999			−0.116974			−0.0584871	−	0.998288i	$-0.518628\pi$
$107$	−1.20999			−0.116974			−0.0584871	+	0.998288i	$0.518628\pi$
$108$	1.89370	+	12.0734i	0.182221	+	1.16177i
$109$	14.1042			1.35094			0.675469	−	0.737388i	$-0.263941\pi$
$109$	14.1042			1.35094			0.675469	+	0.737388i	$0.263941\pi$
$110$		0			0
$111$	−7.84823	+	10.4041i	−0.744921	+	0.987517i
$112$	−6.48113	−	11.2257i	−0.612410	−	1.06072i
$113$	−5.96227	−	10.3270i	−0.560883	−	0.971478i	−0.997420	−	0.0717915i	$-0.977128\pi$
$113$	−5.96227	−	10.3270i	−0.560883	−	0.971478i	0.436537	−	0.899687i	$-0.356205\pi$
$114$	0.913870	+	2.15594i	0.0855917	+	0.201922i
$115$		0			0
$116$	9.11644			0.846440
$117$	1.35194	−	1.39718i	0.124987	−	0.129169i
$118$	8.70388			0.801257
$119$	2.76210	−	4.78410i	0.253201	−	0.438557i
$120$		0			0
$121$	4.58613	+	7.94341i	0.416921	+	0.722128i
$122$	3.98484	+	6.90195i	0.360771	+	0.624873i
$123$	0.308874	+	0.0380816i	0.0278502	+	0.00343370i
$124$	9.05080	−	15.6765i	0.812786	−	1.40779i
$125$		0			0
$126$	17.7826	−	18.3776i	1.58420	−	1.63721i
$127$	7.07871			0.628134			0.314067	−	0.949401i	$-0.398308\pi$
$127$	7.07871			0.628134			0.314067	+	0.949401i	$0.398308\pi$
$128$	2.89130	−	5.00787i	0.255557	−	0.442637i
$129$	0.554512	+	1.30817i	0.0488221	+	0.115178i
$130$		0			0
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$	−3.31661	+	4.39672i	−0.288674	+	0.382685i
$133$	1.32403	−	2.29329i	0.114808	−	0.198853i
$134$	−16.9852			−1.46729
$135$		0			0
$136$	0.992582			0.0851132
$137$	−3.73419	+	6.46781i	−0.319033	+	0.552582i	−0.980287	−	0.197581i	$-0.936692\pi$
$137$	−3.73419	+	6.46781i	−0.319033	+	0.552582i	0.661253	+	0.750163i	$0.270025\pi$
$138$	−10.4229	+	13.8173i	−0.887257	+	1.17621i
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	0.645021	−	0.764165i	$-0.276849\pi$
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	−0.984297	+	0.176522i	$0.943515\pi$
$140$		0			0
$141$	−7.37243	−	17.3925i	−0.620871	−	1.46471i
$142$	6.37985	−	11.0502i	0.535385	−	0.927314i
$143$	0.876139			0.0732664
$144$	−9.23179	−	2.31154i	−0.769316	−	0.192629i
$145$		0			0
$146$	−12.8761	+	22.3021i	−1.06564	+	1.84574i
$147$	−16.6686	−	2.05509i	−1.37480	−	0.169501i
$148$	8.84823	+	15.3256i	0.727320	+	1.25976i
$149$	5.29241	+	9.16673i	0.433571	+	0.750968i	0.997178	−	0.0750759i	$-0.0239199\pi$
$149$	5.29241	+	9.16673i	0.433571	+	0.750968i	−0.563607	+	0.826043i	$0.690587\pi$
$150$		0			0
$151$	−8.84823	+	15.3256i	−0.720059	+	1.24718i	0.240917	+	0.970546i	$0.422552\pi$
$151$	−8.84823	+	15.3256i	−0.720059	+	1.24718i	−0.960976	+	0.276633i	$0.910781\pi$
$152$	0.475800			0.0385925
$153$	−1.11404	−	3.89982i	−0.0900647	−	0.315282i
$154$	11.5242			0.928646
$155$		0			0
$156$	−1.03031	−	2.43064i	−0.0824910	−	0.194607i
$157$	−1.26581	−	2.19245i	−0.101023	−	0.174976i	0.811084	−	0.584930i	$-0.198878\pi$
$157$	−1.26581	−	2.19245i	−0.101023	−	0.174976i	−0.912106	+	0.409954i	$0.865545\pi$
$158$	−10.7900	−	18.6888i	−0.858407	−	1.48680i
$159$	−4.35194	+	5.76922i	−0.345131	+	0.457529i
$160$		0			0
$161$	19.5726			1.54254
$162$	−0.617748	−	18.7650i	−0.0485349	−	1.47432i
$163$	−8.47580			−0.663876			−0.331938	−	0.943301i	$-0.607702\pi$
$163$	−8.47580			−0.663876			−0.331938	+	0.943301i	$0.607702\pi$
$164$	0.211297	−	0.365977i	0.0164995	−	0.0285780i
$165$		0			0
$166$	−12.7863	−	22.1465i	−0.992409	−	1.71890i
$167$	6.36710	+	11.0281i	0.492701	+	0.853383i	0.999965	−	0.00840816i	$-0.00267643\pi$
$167$	6.36710	+	11.0281i	0.492701	+	0.853383i	−0.507264	+	0.861791i	$0.669343\pi$
$168$	−2.02791	−	4.78410i	−0.156457	−	0.369101i
$169$	6.29001	−	10.8946i	0.483847	−	0.838047i
$170$		0			0
$171$	−0.534022	−	1.86940i	−0.0408377	−	0.142957i
$172$	1.92935			0.147111
$173$	11.5242	−	19.9605i	0.876169	−	1.51757i	0.0206561	−	0.999787i	$-0.493424\pi$
$173$	11.5242	−	19.9605i	0.876169	−	1.51757i	0.855513	−	0.517782i	$-0.173242\pi$
$174$	−13.9003	−	1.71380i	−1.05378	−	0.129923i
$175$		0			0
$176$	−2.14435	−	3.71413i	−0.161637	−	0.279963i
$177$	−7.17226	−	0.884280i	−0.539100	−	0.0664666i
$178$	3.12920	−	5.41993i	0.234543	−	0.406241i
$179$	2.22808			0.166534			0.0832672	−	0.996527i	$-0.473465\pi$
$179$	2.22808			0.166534			0.0832672	+	0.996527i	$0.473465\pi$
$180$		0			0
$181$	0.468382			0.0348146			0.0174073	−	0.999848i	$-0.494459\pi$
$181$	0.468382			0.0348146			0.0174073	+	0.999848i	$0.494459\pi$
$182$	−2.76210	+	4.78410i	−0.204740	+	0.354621i
$183$	−2.58242	−	6.09226i	−0.190898	−	0.450353i
$184$	1.75839	+	3.04562i	0.129630	+	0.224526i
$185$		0			0
$186$	−16.7473	+	22.2013i	−1.22797	+	1.62788i
$187$	0.913870	−	1.58287i	0.0668288	−	0.115751i
$188$	−25.6513			−1.87081
$189$	−16.5205	+	13.3371i	−1.20169	+	0.970130i
$190$		0			0
$191$	10.1140	−	17.5180i	0.731826	−	1.26756i	−0.224276	−	0.974526i	$-0.572002\pi$
$191$	10.1140	−	17.5180i	0.731826	−	1.26756i	0.956102	−	0.293034i	$-0.0946650\pi$
$192$	−10.9774	+	14.5524i	−0.792227	+	1.05023i
$193$	−9.96467	−	17.2593i	−0.717273	−	1.24235i	−0.962076	−	0.272780i	$-0.912057\pi$
$193$	−9.96467	−	17.2593i	−0.717273	−	1.24235i	0.244804	−	0.969573i	$-0.421277\pi$
$194$	−14.1648	−	24.5342i	−1.01698	−	1.76145i
$195$		0			0
$196$	−11.4027	+	19.7501i	−0.814482	+	1.41072i
$197$	15.5800			1.11003			0.555015	−	0.831840i	$-0.312712\pi$
$197$	15.5800			1.11003			0.555015	+	0.831840i	$0.312712\pi$
$198$	5.88356	−	6.08043i	0.418126	−	0.432118i
$199$	3.58482			0.254121			0.127061	−	0.991895i	$-0.459446\pi$
$199$	3.58482			0.254121			0.127061	+	0.991895i	$0.459446\pi$
$200$		0			0
$201$	13.9963	+	1.72563i	0.987222	+	0.121716i
$202$	1.53162	+	2.65284i	0.107764	+	0.186653i
$203$	7.91920	+	13.7165i	0.555819	+	0.962707i
$204$	−5.46598	−	0.673910i	−0.382695	−	0.0471831i
$205$		0			0
$206$	−15.6965			−1.09362
$207$	9.99258	−	10.3270i	0.694532	−	0.717773i
$208$	2.05582			0.142545
$209$	0.438069	−	0.758758i	0.0303019	−	0.0524844i
$210$		0			0
$211$	−7.49629	−	12.9840i	−0.516066	−	0.893852i	−0.999826	−	0.0186518i	$-0.994063\pi$
$211$	−7.49629	−	12.9840i	−0.516066	−	0.893852i	0.483760	−	0.875201i	$-0.339271\pi$
$212$	4.90645	+	8.49822i	0.336976	+	0.583660i
$213$	−6.37985	+	8.45755i	−0.437140	+	0.579502i
$214$	1.26210	−	2.18602i	0.0862754	−	0.149433i
$215$		0			0
$216$	−3.55953	−	1.37250i	−0.242195	−	0.0933867i
$217$	31.4487			2.13488
$218$	−14.7116	+	25.4813i	−0.996396	+	1.72581i
$219$	12.8761	−	17.0695i	0.870089	−	1.15345i
$220$		0			0
$221$	0.438069	+	0.758758i	0.0294677	+	0.0510396i
$222$	−10.6103	−	25.0311i	−0.712119	−	1.67998i
$223$	−13.4155	+	23.2363i	−0.898368	+	1.55602i	−0.0687878	+	0.997631i	$0.521913\pi$
$223$	−13.4155	+	23.2363i	−0.898368	+	1.55602i	−0.829580	+	0.558388i	$0.811420\pi$
$224$	33.0410			2.20764
$225$		0			0
$226$	24.8761			1.65474
$227$	0.675970	−	1.17081i	0.0448657	−	0.0777096i	−0.842721	−	0.538351i	$-0.819047\pi$
$227$	0.675970	−	1.17081i	0.0448657	−	0.0777096i	0.887586	+	0.460642i	$0.152381\pi$
$228$	−2.62015	−	0.323043i	−0.173524	−	0.0213940i
$229$	4.11775	+	7.13215i	0.272108	+	0.471306i	0.969402	−	0.245480i	$-0.0789457\pi$
$229$	4.11775	+	7.13215i	0.272108	+	0.471306i	−0.697293	+	0.716786i	$0.745612\pi$
$230$		0			0
$231$	−9.49629	−	1.17081i	−0.624810	−	0.0770339i
$232$	−1.42291	+	2.46456i	−0.0934188	+	0.161806i
$233$	−8.58744			−0.562582			−0.281291	−	0.959623i	$-0.590763\pi$
$233$	−8.58744			−0.562582			−0.281291	+	0.959623i	$0.590763\pi$
$234$	1.11404	+	3.89982i	0.0728270	+	0.254939i
$235$		0			0
$236$	−4.90645	+	8.49822i	−0.319383	+	0.553187i
$237$	6.99258	+	16.4964i	0.454217	+	1.07156i
$238$	5.76210	+	9.98025i	0.373501	+	0.646923i
$239$	11.9623	+	20.7193i	0.773775	+	1.34022i	0.935480	+	0.353378i	$0.114967\pi$
$239$	11.9623	+	20.7193i	0.773775	+	1.34022i	−0.161706	+	0.986839i	$0.551700\pi$
$240$		0			0
$241$	3.12015	−	5.40426i	0.200987	−	0.348119i	−0.747860	−	0.663857i	$-0.768919\pi$
$241$	3.12015	−	5.40426i	0.200987	−	0.348119i	0.948847	+	0.315737i	$0.102252\pi$
$242$	−19.1345			−1.23001
$243$	−1.39741	+	15.5257i	−0.0896438	+	0.995974i
$244$	−8.98516			−0.575216
$245$		0			0
$246$	−0.390976	+	0.518303i	−0.0249277	+	0.0330458i
$247$	0.209991	+	0.363716i	0.0133614	+	0.0231427i
$248$	2.82534	+	4.89363i	0.179409	+	0.310746i
$249$	8.28630	+	19.5484i	0.525123	+	1.23883i
$250$		0			0
$251$	−28.5726			−1.80349			−0.901743	−	0.432272i	$-0.857712\pi$
$251$	−28.5726			−1.80349			−0.901743	+	0.432272i	$0.857712\pi$
$252$	7.91920	+	27.7221i	0.498863	+	1.74633i
$253$	6.47580			0.407130
$254$	−7.38356	+	12.7887i	−0.463286	+	0.802434i
$255$		0			0
$256$	−4.49258	−	7.78138i	−0.280786	−	0.486336i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$	−2.94178	−	0.362697i	−0.183147	−	0.0225805i
$259$	−15.3724	+	26.6258i	−0.955196	+	1.65445i
$260$		0			0
$261$	11.2802	+	2.82444i	0.698226	+	0.174828i
$262$	−12.5168			−0.773289
$263$	15.9344	−	27.5991i	0.982555	−	1.70183i	0.330220	−	0.943904i	$-0.392877\pi$
$263$	15.9344	−	27.5991i	0.982555	−	1.70183i	0.652335	−	0.757931i	$-0.273789\pi$
$264$	−0.670955	−	1.58287i	−0.0412944	−	0.0974188i
$265$		0			0
$266$	2.76210	+	4.78410i	0.169355	+	0.293332i
$267$	−3.12920	+	4.14827i	−0.191504	+	0.253870i
$268$	9.57468	−	16.5838i	0.584867	−	1.01302i
$269$	−31.4971			−1.92041			−0.960207	−	0.279289i	$-0.909901\pi$
$269$	−31.4971			−1.92041			−0.960207	+	0.279289i	$0.909901\pi$
$270$		0			0
$271$	−3.24030			−0.196834			−0.0984172	−	0.995145i	$-0.531378\pi$
$271$	−3.24030			−0.196834			−0.0984172	+	0.995145i	$0.531378\pi$
$272$	2.14435	−	3.71413i	0.130020	−	0.225202i
$273$	2.76210	−	3.66162i	0.167170	−	0.221612i
$274$	−7.79001	−	13.4927i	−0.470612	−	0.815123i
$275$		0			0
$276$	−7.61534	−	17.9656i	−0.458390	−	1.08140i
$277$	−2.79241	+	4.83660i	−0.167780	+	0.290603i	−0.937639	−	0.347611i	$-0.886993\pi$
$277$	−2.79241	+	4.83660i	−0.167780	+	0.290603i	0.769859	+	0.638214i	$0.220326\pi$
$278$	16.6890			1.00094
$279$	16.0558	−	16.5931i	0.961237	−	0.993402i
$280$		0			0
$281$	12.0521	−	20.8749i	0.718969	−	1.24529i	−0.242440	−	0.970166i	$-0.577948\pi$
$281$	12.0521	−	20.8749i	0.718969	−	1.24529i	0.961409	−	0.275124i	$-0.0887188\pi$
$282$	39.1120	+	4.82218i	2.32908	+	0.287157i
$283$	−5.27114	−	9.12989i	−0.313337	−	0.542715i	0.665746	−	0.746179i	$-0.268114\pi$
$283$	−5.27114	−	9.12989i	−0.313337	−	0.542715i	−0.979083	+	0.203463i	$0.934780\pi$
$284$	7.19275	+	12.4582i	0.426811	+	0.739259i
$285$		0			0
$286$	−0.913870	+	1.58287i	−0.0540383	+	0.0935970i
$287$	0.734191			0.0433379
$288$	16.8687	−	17.4332i	0.993999	−	1.02726i
$289$	−15.1723			−0.892486
$290$		0			0
$291$	9.17968	+	21.6560i	0.538122	+	1.26950i
$292$	−14.5168	−	25.1438i	−0.849530	−	1.47143i
$293$	9.49629	+	16.4481i	0.554779	+	0.960906i	0.997921	+	0.0644541i	$0.0205306\pi$
$293$	9.49629	+	16.4481i	0.554779	+	0.960906i	−0.443141	+	0.896452i	$0.646136\pi$
$294$	21.0992	−	27.9705i	1.23053	−	1.63127i
$295$		0			0
$296$	−5.52420			−0.321088
$297$	−5.46598	+	4.41271i	−0.317168	+	0.256052i
$298$	−22.0813			−1.27914
$299$	−1.55211	+	2.68833i	−0.0897607	+	0.155470i
$300$		0			0
$301$	1.67597	+	2.90286i	0.0966013	+	0.167318i
$302$	−18.4586	−	31.9712i	−1.06217	−	1.83973i
$303$	−0.992582	−	2.34163i	−0.0570223	−	0.134523i
$304$	1.02791	−	1.78039i	0.0589546	−	0.102112i
$305$		0			0
$306$	8.20759	+	2.05509i	0.469197	+	0.117482i
$307$	−29.4791			−1.68246			−0.841229	−	0.540679i	$-0.818167\pi$
$307$	−29.4791			−1.68246			−0.841229	+	0.540679i	$0.818167\pi$
$308$	−6.49629	+	11.2519i	−0.370161	+	0.641137i
$309$	12.9344	+	1.59470i	0.735810	+	0.0907193i
$310$		0			0
$311$	4.70628	+	8.15152i	0.266869	+	0.462230i	0.968052	−	0.250751i	$-0.0806776\pi$
$311$	4.70628	+	8.15152i	0.266869	+	0.462230i	−0.701183	+	0.712982i	$0.747344\pi$
$312$	0.817917	+	0.100842i	0.0463055	+	0.00570908i
$313$	5.81050	−	10.0641i	0.328429	−	0.568855i	−0.653771	−	0.756692i	$-0.726814\pi$
$313$	5.81050	−	10.0641i	0.328429	−	0.568855i	0.982200	+	0.187837i	$0.0601476\pi$
$314$	5.28128			0.298040
$315$		0			0
$316$	24.3297			1.36865
$317$	−4.58984	+	7.94984i	−0.257791	+	0.446507i	−0.965650	−	0.259847i	$-0.916328\pi$
$317$	−4.58984	+	7.94984i	−0.257791	+	0.446507i	0.707859	+	0.706354i	$0.249661\pi$
$318$	−5.88356	−	13.8801i	−0.329934	−	0.778355i
$319$	2.62015	+	4.53824i	0.146700	+	0.254092i
$320$		0			0
$321$	−1.26210	+	1.67312i	−0.0704435	+	0.0933846i
$322$	−20.4155	+	35.3607i	−1.13771	+	1.97057i
$323$	0.876139			0.0487497
$324$	18.6699	+	9.97484i	1.03721	+	0.554158i
$325$		0			0
$326$	8.84081	−	15.3127i	0.489647	−	0.848094i
$327$	14.7116	−	19.5027i	0.813554	−	1.07850i
$328$	0.0659593	+	0.114245i	0.00364199	+	0.00630812i
$329$	−22.2826	−	38.5946i	−1.22848	−	2.12779i
$330$		0			0
$331$	3.61033	−	6.25327i	0.198442	−	0.343711i	−0.749582	−	0.661912i	$-0.769745\pi$
$331$	3.61033	−	6.25327i	0.198442	−	0.343711i	0.948023	+	0.318201i	$0.103079\pi$
$332$	28.8310			1.58231
$333$	6.20017	+	21.7044i	0.339767	+	1.18939i
$334$	−26.5652			−1.45358
$335$		0			0
$336$	−22.2826	−	2.74726i	−1.21561	−	0.149875i
$337$	1.14195	+	1.97791i	0.0622059	+	0.107744i	0.895451	−	0.445160i	$-0.146853\pi$
$337$	1.14195	+	1.97791i	0.0622059	+	0.107744i	−0.833245	+	0.552904i	$0.813520\pi$
$338$	13.1218	+	22.7276i	0.713731	+	1.23622i
$339$	−20.4987	−	2.52732i	−1.11334	−	0.137265i
$340$		0			0
$341$	10.4051			0.563470
$342$	3.93436	+	0.985122i	0.212746	+	0.0532693i
$343$	−11.0181			−0.594921
$344$	−0.301136	+	0.521583i	−0.0162362	+	0.0281219i
$345$		0			0
$346$	24.0410	+	41.6402i	1.29245	+	2.23859i
$347$	−0.354343	−	0.613740i	−0.0190221	−	0.0329473i	0.856358	−	0.516383i	$-0.172722\pi$
$347$	−0.354343	−	0.613740i	−0.0190221	−	0.0329473i	−0.875380	+	0.483436i	$0.839389\pi$
$348$	9.50904	−	12.6058i	0.509738	−	0.675743i
$349$	10.6723	−	18.4849i	0.571273	−	0.989474i	−0.425163	−	0.905117i	$-0.639783\pi$
$349$	10.6723	−	18.4849i	0.571273	−	0.989474i	0.996436	−	0.0843569i	$-0.0268836\pi$
$350$		0			0
$351$	−0.521796	−	3.32675i	−0.0278514	−	0.177569i
$352$	10.9320			0.582675
$353$	−5.04840	+	8.74408i	−0.268699	+	0.465401i	−0.968526	−	0.248912i	$-0.919927\pi$
$353$	−5.04840	+	8.74408i	−0.268699	+	0.465401i	0.699827	+	0.714312i	$0.253260\pi$
$354$	9.07871	−	12.0353i	0.482528	−	0.639671i
$355$		0			0
$356$	3.52791	+	6.11052i	0.186979	+	0.323857i
$357$	−3.73419	−	8.80944i	−0.197634	−	0.466245i
$358$	−2.32403	+	4.02534i	−0.122829	+	0.212746i
$359$	30.5578			1.61278			0.806388	−	0.591386i	$-0.201419\pi$
$359$	30.5578			1.61278			0.806388	+	0.591386i	$0.201419\pi$
$360$		0			0
$361$	−18.5800			−0.977896
$362$	−0.488553	+	0.846198i	−0.0256778	+	0.0444752i
$363$	15.7674	+	1.94399i	0.827576	+	0.102033i
$364$	−3.11404	−	5.39367i	−0.163220	−	0.282705i
$365$		0			0
$366$	13.7002	+	1.68912i	0.716119	+	0.0882916i
$367$	−3.58984	+	6.21778i	−0.187388	+	0.324566i	−0.944379	−	0.328860i	$-0.893336\pi$
$367$	−3.58984	+	6.21778i	−0.187388	+	0.324566i	0.756991	+	0.653426i	$0.226669\pi$
$368$	15.1952			0.792102
$369$	0.374833	−	0.387376i	0.0195130	−	0.0201660i
$370$		0			0
$371$	−8.52420	+	14.7643i	−0.442554	+	0.766527i
$372$	−12.2361	−	28.8666i	−0.634414	−	1.49666i
$373$	−10.9623	−	18.9872i	−0.567605	−	0.983120i	−0.996802	−	0.0799096i	$-0.974537\pi$
$373$	−10.9623	−	18.9872i	−0.567605	−	0.983120i	0.429197	−	0.903211i	$-0.358796\pi$
$374$	1.90645	+	3.30207i	0.0985803	+	0.170746i
$375$		0			0
$376$	4.00371	−	6.93463i	0.206476	−	0.357626i
$377$	−2.51197			−0.129373
$378$	−6.86339	−	43.7581i	−0.353014	−	2.25067i
$379$	−17.3929			−0.893414			−0.446707	−	0.894680i	$-0.647403\pi$
$379$	−17.3929			−0.893414			−0.446707	+	0.894680i	$0.647403\pi$
$380$		0			0
$381$	7.38356	−	9.78813i	0.378271	−	0.501461i
$382$	21.0992	+	36.5449i	1.07953	+	1.86980i
$383$	0.237900	+	0.412055i	0.0121561	+	0.0210550i	0.872039	−	0.489436i	$-0.162797\pi$
$383$	0.237900	+	0.412055i	0.0121561	+	0.0210550i	−0.859883	+	0.510491i	$0.829464\pi$
$384$	−3.90886	−	9.22149i	−0.199473	−	0.470582i
$385$		0			0
$386$	41.5752			2.11612
$387$	2.38727	+	0.597746i	0.121352	+	0.0303852i
$388$	31.9394			1.62148
$389$	2.79372	−	4.83886i	0.141647	−	0.245340i	−0.786470	−	0.617629i	$-0.788094\pi$
$389$	2.79372	−	4.83886i	0.141647	−	0.245340i	0.928117	+	0.372289i	$0.121427\pi$
$390$		0			0
$391$	3.23790	+	5.60821i	0.163748	+	0.283619i
$392$	−3.55953	−	6.16528i	−0.179783	−	0.311394i
$393$	10.3142	+	1.27166i	0.520283	+	0.0641466i
$394$	−16.2510	+	28.1475i	−0.818712	+	1.41805i
$395$		0			0
$396$	2.62015	+	9.17213i	0.131668	+	0.460917i
$397$	−3.75228			−0.188321			−0.0941607	−	0.995557i	$-0.530017\pi$
$397$	−3.75228			−0.188321			−0.0941607	+	0.995557i	$0.530017\pi$
$398$	−3.73921	+	6.47649i	−0.187429	+	0.324637i
$399$	−1.79001	−	4.22286i	−0.0896125	−	0.211407i
$400$		0			0
$401$	−11.7826	−	20.4080i	−0.588394	−	1.01913i	−0.994443	−	0.105278i	$-0.966427\pi$
$401$	−11.7826	−	20.4080i	−0.588394	−	1.01913i	0.406048	−	0.913852i	$-0.366906\pi$
$402$	−17.7166	+	23.4863i	−0.883625	+	1.17139i
$403$	−2.49389	+	4.31954i	−0.124229	+	0.215172i
$404$	−3.45355			−0.171820
$405$		0			0
$406$	−33.0410			−1.63980
$407$	−5.08613	+	8.80944i	−0.252110	+	0.436668i
$408$	1.03533	−	1.37250i	0.0512563	−	0.0679488i
$409$	−0.524200	−	0.907940i	−0.0259200	−	0.0448948i	0.852774	−	0.522279i	$-0.174918\pi$
$409$	−0.524200	−	0.907940i	−0.0259200	−	0.0448948i	−0.878694	+	0.477385i	$0.841585\pi$
$410$		0			0
$411$	5.04840	+	11.9098i	0.249019	+	0.587468i
$412$	8.84823	−	15.3256i	0.435921	−	0.755037i
$413$	−17.0484			−0.838897
$414$	8.23419	+	28.8247i	0.404688	+	1.41666i
$415$		0			0
$416$	−2.62015	+	4.53824i	−0.128464	+	0.222505i
$417$	−13.7523	−	1.69554i	−0.673452	−	0.0830310i
$418$	0.913870	+	1.58287i	0.0446988	+	0.0774207i
$419$	12.9599	+	22.4471i	0.633131	+	1.09661i	0.986908	+	0.161285i	$0.0515638\pi$
$419$	12.9599	+	22.4471i	0.633131	+	1.09661i	−0.353777	+	0.935330i	$0.615103\pi$
$420$		0			0
$421$	−3.82032	+	6.61699i	−0.186191	+	0.322492i	−0.943977	−	0.330011i	$-0.892948\pi$
$421$	−3.82032	+	6.61699i	−0.186191	+	0.322492i	0.757786	+	0.652503i	$0.226281\pi$
$422$	31.2765			1.52252
$423$	−31.7395	−	7.94724i	−1.54323	−	0.386408i
$424$	−3.06324			−0.148764
$425$		0			0
$426$	−8.62517	−	20.3479i	−0.417891	−	0.985858i
$427$	−7.80516	−	13.5189i	−0.377718	−	0.654227i
$428$	1.42291	+	2.46456i	0.0687791	+	0.119129i
$429$	0.913870	−	1.21149i	0.0441220	−	0.0584911i
$430$		0			0
$431$	7.98516			0.384632			0.192316	−	0.981333i	$-0.438400\pi$
$431$	7.98516			0.384632			0.192316	+	0.981333i	$0.438400\pi$
$432$	−12.8257	+	10.3542i	−0.617075	+	0.498168i
$433$	12.5120			0.601287			0.300644	−	0.953737i	$-0.402799\pi$
$433$	12.5120			0.601287			0.300644	+	0.953737i	$0.402799\pi$
$434$	−32.8031	+	56.8166i	−1.57460	+	2.72728i
$435$		0			0
$436$	−16.5861	−	28.7280i	−0.794332	−	1.37582i
$437$	1.55211	+	2.68833i	0.0742474	+	0.128600i
$438$	17.4078	+	41.0671i	0.831775	+	1.96226i
$439$	4.38225	−	7.59028i	0.209153	−	0.362264i	−0.742295	−	0.670074i	$-0.766263\pi$
$439$	4.38225	−	7.59028i	0.209153	−	0.362264i	0.951448	+	0.307809i	$0.0995958\pi$
$440$		0			0
$441$	−20.2281	+	20.9049i	−0.963242	+	0.995474i
$442$	−1.82774			−0.0869367
$443$	1.83548	−	3.17914i	0.0872062	−	0.151046i	−0.819123	−	0.573618i	$-0.805539\pi$
$443$	1.83548	−	3.17914i	0.0872062	−	0.151046i	0.906329	+	0.422572i	$0.138873\pi$
$444$	30.4208	+	3.75064i	1.44371	+	0.177997i
$445$		0			0
$446$	−27.9865	−	48.4740i	−1.32520	−	2.29531i
$447$	18.1957	+	2.24338i	0.860626	+	0.106108i
$448$	−21.5016	+	37.2419i	−1.01586	+	1.75951i
$449$	28.1723			1.32953			0.664766	−	0.747052i	$-0.268531\pi$
$449$	28.1723			1.32953			0.664766	+	0.747052i	$0.268531\pi$
$450$		0			0
$451$	0.242915			0.0114384
$452$	−14.0229	+	24.2884i	−0.659581	+	1.14243i
$453$	11.9623	+	28.2205i	0.562036	+	1.32592i
$454$	1.41016	+	2.44247i	0.0661821	+	0.114631i
$455$		0			0
$456$	0.496291	−	0.657916i	0.0232409	−	0.0308097i
$457$	17.6308	−	30.5375i	0.824735	−	1.42848i	−0.0773867	−	0.997001i	$-0.524658\pi$
$457$	17.6308	−	30.5375i	0.824735	−	1.42848i	0.902122	−	0.431482i	$-0.142009\pi$
$458$	−17.1803			−0.802784
$459$	−6.55451	−	2.52732i	−0.305938	−	0.117965i
$460$		0			0
$461$	−17.3384	+	30.0310i	−0.807530	+	1.39868i	0.107039	+	0.994255i	$0.465863\pi$
$461$	−17.3384	+	30.0310i	−0.807530	+	1.39868i	−0.914570	+	0.404428i	$0.867470\pi$
$462$	12.0205	−	15.9352i	0.559244	−	0.741371i
$463$	3.72437	+	6.45080i	0.173086	+	0.299794i	0.939497	−	0.342556i	$-0.111293\pi$
$463$	3.72437	+	6.45080i	0.173086	+	0.299794i	−0.766411	+	0.642350i	$0.777959\pi$
$464$	6.14806	+	10.6488i	0.285417	+	0.494356i
$465$		0			0
$466$	8.95725	−	15.5144i	0.414937	−	0.718692i
$467$	−29.9655			−1.38664			−0.693319	−	0.720630i	$-0.743852\pi$
$467$	−29.9655			−1.38664			−0.693319	+	0.720630i	$0.743852\pi$
$468$	−4.43567	−	1.11064i	−0.205039	−	0.0513395i
$469$	33.2691			1.53622
$470$		0			0
$471$	−4.35194	−	0.536558i	−0.200527	−	0.0247233i
$472$	−1.53162	−	2.65284i	−0.0704984	−	0.122107i
$473$	0.554512	+	0.960443i	0.0254965	+	0.0441612i
$474$	−37.0968	−	4.57373i	−1.70391	−	0.210078i
$475$		0			0
$476$	−12.9926			−0.595514
$477$	3.43807	+	12.0353i	0.157418	+	0.551061i
$478$	−49.9097			−2.28282
$479$	3.99258	−	6.91535i	0.182426	−	0.315971i	−0.760280	−	0.649595i	$-0.774938\pi$
$479$	3.99258	−	6.91535i	0.182426	−	0.315971i	0.942706	+	0.333625i	$0.108272\pi$
$480$		0			0
$481$	−2.43807	−	4.22286i	−0.111166	−	0.192546i
$482$	6.50904	+	11.2740i	0.296479	+	0.513516i
$483$	20.4155	−	27.0641i	0.928937	−	1.23146i
$484$	10.7863	−	18.6824i	0.490286	−	0.849201i
$485$		0			0
$486$	−26.5918	−	18.7189i	−1.20623	−	0.849108i
$487$	11.9442			0.541243			0.270621	−	0.962686i	$-0.412771\pi$
$487$	11.9442			0.541243			0.270621	+	0.962686i	$0.412771\pi$
$488$	1.40242	−	2.42907i	0.0634847	−	0.109959i
$489$	−8.84081	+	11.7200i	−0.399795	+	0.529995i
$490$		0			0
$491$	4.61033	+	7.98533i	0.208061	+	0.360373i	0.951104	−	0.308872i	$-0.0999513\pi$
$491$	4.61033	+	7.98533i	0.208061	+	0.360373i	−0.743042	+	0.669244i	$0.766618\pi$
$492$	−0.285660	−	0.673910i	−0.0128786	−	0.0303822i
$493$	−2.62015	+	4.53824i	−0.118006	+	0.204392i
$494$	−0.876139			−0.0394193
$495$		0			0
$496$	24.4152			1.09627
$497$	−12.4963	+	21.6442i	−0.560535	+	0.970876i
$498$	−43.9602	−	5.41993i	−1.96990	−	0.242873i
$499$	−15.0861	−	26.1299i	−0.675348	−	1.16974i	−0.976367	−	0.216119i	$-0.930660\pi$
$499$	−15.0861	−	26.1299i	−0.675348	−	1.16974i	0.301019	−	0.953618i	$-0.402673\pi$
$500$		0			0
$501$	21.8905	+	2.69892i	0.977996	+	0.120579i
$502$	29.8031	−	51.6204i	1.33018	−	2.30393i
$503$	10.5981			0.472546			0.236273	−	0.971687i	$-0.424074\pi$
$503$	10.5981			0.472546			0.236273	+	0.971687i	$0.424074\pi$
$504$	−8.73048	−	2.18602i	−0.388887	−	0.0973731i
$505$		0			0
$506$	−6.75468	+	11.6995i	−0.300282	+	0.520104i
$507$	−8.50371	−	20.0613i	−0.377663	−	0.890955i
$508$	−8.32435	−	14.4182i	−0.369333	−	0.639704i
$509$	−14.3761	−	24.9002i	−0.637211	−	1.10368i	−0.986042	−	0.166496i	$-0.946755\pi$
$509$	−14.3761	−	24.9002i	−0.637211	−	1.10368i	0.348831	−	0.937186i	$-0.386579\pi$
$510$		0			0
$511$	25.2207	−	43.6835i	1.11570	−	1.93244i
$512$	30.3094			1.33950
$513$	−3.14195	−	1.21149i	−0.138720	−	0.0534884i
$514$	37.5503			1.65627
$515$		0			0
$516$	2.01243	−	2.66781i	0.0885924	−	0.117444i
$517$	−7.37243	−	12.7694i	−0.324239	−	0.561599i
$518$	−32.0689	−	55.5449i	−1.40903	−	2.44050i
$519$	−15.5800	−	36.7553i	−0.683887	−	1.61338i
$520$		0			0
$521$	−36.0942			−1.58132			−0.790658	−	0.612259i	$-0.790261\pi$
$521$	−36.0942			−1.58132			−0.790658	+	0.612259i	$0.790261\pi$
$522$	−16.8687	+	17.4332i	−0.738324	+	0.763030i
$523$	−11.1297			−0.486669			−0.243334	−	0.969942i	$-0.578241\pi$
$523$	−11.1297			−0.486669			−0.243334	+	0.969942i	$0.578241\pi$
$524$	7.05582	−	12.2210i	0.308235	−	0.533878i
$525$		0			0
$526$	33.2411	+	57.5754i	1.44938	+	2.51041i
$527$	5.20257	+	9.01112i	0.226628	+	0.392531i
$528$	−7.37243	−	0.908959i	−0.320844	−	0.0395574i
$529$	0.0279088	−	0.0483395i	0.00121343	−	0.00210172i
$530$		0			0
$531$	−8.70388	+	8.99513i	−0.377716	+	0.390355i
$532$	−6.22808			−0.270021
$533$	−0.0582214	+	0.100842i	−0.00252185	+	0.00436797i
$534$	−4.23048	−	9.98025i	−0.183071	−	0.431888i
$535$		0			0
$536$	2.98887	+	5.17688i	0.129100	+	0.223607i
$537$	2.32403	−	3.08089i	0.100289	−	0.132950i
$538$	32.8536	−	56.9040i	1.41642	−	2.45331i
$539$	−13.1090			−0.564646
$540$		0			0
$541$	−34.7374			−1.49348			−0.746740	−	0.665116i	$-0.768382\pi$
$541$	−34.7374			−1.49348			−0.746740	+	0.665116i	$0.768382\pi$
$542$	3.37985	−	5.85407i	0.145177	−	0.251454i
$543$	0.488553	−	0.647658i	0.0209658	−	0.0277937i
$544$	5.46598	+	9.46735i	0.234352	+	0.405909i
$545$		0			0
$546$	3.73419	+	8.80944i	0.159809	+	0.377009i
$547$	−1.35727	+	2.35087i	−0.0580328	+	0.100516i	−0.893582	−	0.448899i	$-0.851816\pi$
$547$	−1.35727	+	2.35087i	−0.0580328	+	0.100516i	0.835549	+	0.549415i	$0.185149\pi$
$548$	17.5652			0.750347
$549$	−11.1177	−	2.78377i	−0.474494	−	0.118808i
$550$		0			0
$551$	−1.25599	+	2.17543i	−0.0535068	+	0.0926766i
$552$	6.04547	+	0.745356i	0.257312	+	0.0317245i
$553$	21.1345	+	36.6061i	0.898732	+	1.55665i
$554$	−5.82534	−	10.0898i	−0.247495	−	0.428674i
$555$		0			0
$556$	−9.40776	+	16.2947i	−0.398978	+	0.691050i
$557$	8.93676			0.378663			0.189331	−	0.981913i	$-0.439368\pi$
$557$	8.93676			0.378663			0.189331	+	0.981913i	$0.439368\pi$
$558$	13.2305	+	46.3148i	0.560091	+	1.96066i
$559$	−0.531618			−0.0224850
$560$		0			0
$561$	−1.23550	−	2.91469i	−0.0521627	−	0.123059i
$562$	25.1423	+	43.5477i	1.06056	+	1.83695i
$563$	−4.68130	−	8.10826i	−0.197293	−	0.341722i	0.750357	−	0.661033i	$-0.229882\pi$
$563$	−4.68130	−	8.10826i	−0.197293	−	0.341722i	−0.947650	+	0.319311i	$0.896549\pi$
$564$	−26.7560	+	35.4695i	−1.12663	+	1.49354i
$565$		0			0
$566$	21.9926			0.924417
$567$	1.20999	+	36.7553i	0.0508149	+	1.54358i
$568$	−4.49064			−0.188423
$569$	−17.9368	+	31.0674i	−0.751948	+	1.30241i	0.194929	+	0.980817i	$0.437552\pi$
$569$	−17.9368	+	31.0674i	−0.751948	+	1.30241i	−0.946877	+	0.321595i	$0.895781\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−1.03031	−	1.78455i	−0.0430795	−	0.0746159i
$573$	−13.6736	−	32.2577i	−0.571221	−	1.34758i
$574$	−0.765809	+	1.32642i	−0.0319643	+	0.0553637i
$575$		0			0
$576$	8.67226	+	30.3582i	0.361344	+	1.26493i
$577$	−1.35675			−0.0564821			−0.0282411	−	0.999601i	$-0.508991\pi$
$577$	−1.35675			−0.0564821			−0.0282411	+	0.999601i	$0.508991\pi$
$578$	15.8257	−	27.4108i	0.658260	−	1.14014i
$579$	−34.2592	−	4.22388i	−1.42377	−	0.175538i
$580$		0			0
$581$	25.0447	+	43.3787i	1.03903	+	1.79965i
$582$	−48.6997	−	6.00427i	−2.01867	−	0.248885i
$583$	−2.82032	+	4.88494i	−0.116806	+	0.202314i
$584$	9.06324			0.375039
$585$		0			0
$586$	−39.6210			−1.63673
$587$	14.3950	−	24.9329i	0.594145	−	1.02909i	−0.399521	−	0.916724i	$-0.630824\pi$
$587$	14.3950	−	24.9329i	0.594145	−	1.02909i	0.993667	−	0.112366i	$-0.0358430\pi$
$588$	15.4158	+	36.3679i	0.635737	+	1.49979i
$589$	2.49389	+	4.31954i	0.102759	+	0.177984i
$590$		0			0
$591$	16.2510	−	21.5434i	0.668476	−	0.886176i
$592$	−11.9344	+	20.6709i	−0.490499	+	0.849570i
$593$	−30.9171			−1.26961			−0.634807	−	0.772671i	$-0.718920\pi$
$593$	−30.9171			−1.26961			−0.634807	+	0.772671i	$0.718920\pi$
$594$	−2.27082	−	14.4778i	−0.0931730	−	0.594032i
$595$		0			0
$596$	12.4474	−	21.5596i	0.509867	−	0.883115i
$597$	3.73921	−	4.95694i	0.153035	−	0.202874i
$598$	−3.23790	−	5.60821i	−0.132408	−	0.229337i
$599$	−0.696460	−	1.20630i	−0.0284566	−	0.0492882i	0.851446	−	0.524442i	$-0.175726\pi$
$599$	−0.696460	−	1.20630i	−0.0284566	−	0.0492882i	−0.879903	+	0.475153i	$0.842393\pi$
$600$		0			0
$601$	−4.41256	+	7.64279i	−0.179992	+	0.311756i	−0.941878	−	0.335956i	$-0.890941\pi$
$601$	−4.41256	+	7.64279i	−0.179992	+	0.311756i	0.761885	+	0.647712i	$0.224274\pi$
$602$	−6.99258			−0.284996
$603$	16.9852	−	17.5535i	0.691689	−	0.714835i
$604$	41.6210			1.69353
$605$		0			0
$606$	5.26581	+	0.649230i	0.213909	+	0.0263732i
$607$	−1.07839	−	1.86783i	−0.0437706	−	0.0758129i	0.843310	−	0.537427i	$-0.180604\pi$
$607$	−1.07839	−	1.86783i	−0.0437706	−	0.0758129i	−0.887081	+	0.461614i	$0.847270\pi$
$608$	2.62015	+	4.53824i	0.106261	+	0.184050i
$609$	27.2268	+	3.35683i	1.10328	+	0.136026i
$610$		0			0
$611$	7.06804			0.285942
$612$	−6.63322	+	6.85518i	−0.268132	+	0.277104i
$613$	9.57521			0.386739			0.193370	−	0.981126i	$-0.438058\pi$
$613$	9.57521			0.386739			0.193370	+	0.981126i	$0.438058\pi$
$614$	30.7486	−	53.2581i	1.24091	−	2.14932i
$615$		0			0
$616$	−2.02791	−	3.51244i	−0.0817068	−	0.141520i
$617$	−18.8384	−	32.6291i	−0.758406	−	1.31360i	−0.943663	−	0.330907i	$-0.892645\pi$
$617$	−18.8384	−	32.6291i	−0.758406	−	1.31360i	0.185258	−	0.982690i	$-0.440688\pi$
$618$	−16.3724	+	21.7044i	−0.658596	+	0.873078i
$619$	−8.55211	+	14.8127i	−0.343738	+	0.595372i	−0.985124	−	0.171847i	$-0.945027\pi$
$619$	−8.55211	+	14.8127i	−0.343738	+	0.595372i	0.641385	+	0.767219i	$0.278360\pi$
$620$		0			0
$621$	−3.85675	−	24.5890i	−0.154766	−	0.986722i
$622$	−19.6358			−0.787325
$623$	−6.12920	+	10.6161i	−0.245561	+	0.425324i
$624$	2.14435	−	2.84269i	0.0858428	−	0.113799i
$625$		0			0
$626$	12.1215	+	20.9950i	0.484471	+	0.839128i
$627$	−0.592243	−	1.39718i	−0.0236519	−	0.0557979i
$628$	−2.97711	+	5.15650i	−0.118799	+	0.205767i
$629$	−10.1723			−0.405595
$630$		0			0
$631$	33.1090			1.31805			0.659025	−	0.752121i	$-0.270969\pi$
$631$	33.1090			1.31805			0.659025	+	0.752121i	$0.270969\pi$
$632$	−3.79743	+	6.57734i	−0.151054	+	0.261632i
$633$	−25.7728	−	3.17757i	−1.02438	−	0.126297i
$634$	−9.57500	−	16.5844i	−0.380272	−	0.658650i
$635$		0			0
$636$	16.8687	+	2.07977i	0.668888	+	0.0824684i
$637$	3.14195	−	5.44201i	0.124489	−	0.215620i
$638$	−10.9320			−0.432800
$639$	5.04013	+	17.6436i	0.199385	+	0.697968i
$640$		0			0
$641$	11.5763	−	20.0508i	0.457237	−	0.791957i	−0.541577	−	0.840651i	$-0.682173\pi$
$641$	11.5763	−	20.0508i	0.457237	−	0.791957i	0.998814	+	0.0486939i	$0.0155059\pi$
$642$	−1.70628	−	4.02534i	−0.0673416	−	0.158867i
$643$	21.5319	+	37.2944i	0.849137	+	1.47075i	0.881980	+	0.471287i	$0.156211\pi$
$643$	21.5319	+	37.2944i	0.849137	+	1.47075i	−0.0328430	+	0.999461i	$0.510456\pi$
$644$	−23.0168	−	39.8662i	−0.906988	−	1.57095i
$645$		0			0
$646$	−0.913870	+	1.58287i	−0.0359557	+	0.0622771i
$647$	20.6439			0.811595			0.405798	−	0.913963i	$-0.366994\pi$
$647$	20.6439			0.811595			0.405798	+	0.913963i	$0.366994\pi$
$648$	−5.61065	+	3.49035i	−0.220407	+	0.137114i
$649$	−5.64064			−0.221415
$650$		0			0
$651$	32.8031	−	43.4859i	1.28565	−	1.70435i
$652$	9.96728	+	17.2638i	0.390349	+	0.676104i
$653$	3.41758	+	5.91942i	0.133740	+	0.231645i	0.925116	−	0.379686i	$-0.123968\pi$
$653$	3.41758	+	5.91942i	0.133740	+	0.231645i	−0.791375	+	0.611331i	$0.790635\pi$
$654$	19.8892	+	46.9212i	0.777730	+	1.83476i
$655$		0			0
$656$	0.569988			0.0222543
$657$	−10.1723	−	35.6091i	−0.396858	−	1.38924i
$658$	92.9688			3.62430
$659$	13.4307	−	23.2626i	0.523184	−	0.906181i	−0.476452	−	0.879200i	$-0.658077\pi$
$659$	13.4307	−	23.2626i	0.523184	−	0.906181i	0.999636	−	0.0269806i	$-0.00858924\pi$
$660$		0			0
$661$	1.06063	+	1.83706i	0.0412535	+	0.0714532i	0.885915	−	0.463848i	$-0.153532\pi$
$661$	1.06063	+	1.83706i	0.0412535	+	0.0714532i	−0.844661	+	0.535301i	$0.820198\pi$
$662$	7.53162	+	13.0451i	0.292725	+	0.507014i
$663$	1.50611	+	0.185691i	0.0584926	+	0.00721165i
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$		0			0
$666$	−45.6792	−	11.4376i	−1.77003	−	0.443198i
$667$	−18.5667			−0.718907
$668$	14.9750	−	25.9375i	0.579401	−	1.00355i
$669$	18.1369	+	42.7874i	0.701214	+	1.65425i
$670$		0			0
$671$	−2.58242	−	4.47288i	−0.0996933	−	0.172674i
$672$	34.4639	−	45.6876i	1.32947	−	1.76244i
$673$	17.4102	−	30.1553i	0.671112	−	1.16240i	−0.306477	−	0.951878i	$-0.599150\pi$
$673$	17.4102	−	30.1553i	0.671112	−	1.16240i	0.977589	−	0.210523i	$-0.0675165\pi$
$674$	−4.76450			−0.183522
$675$		0			0
$676$	−29.5874			−1.13798
$677$	−12.3421	+	21.3772i	−0.474346	+	0.821592i	−0.999569	−	0.0293735i	$-0.990649\pi$
$677$	−12.3421	+	21.3772i	−0.474346	+	0.821592i	0.525222	+	0.850965i	$0.323982\pi$
$678$	25.9474	−	34.3976i	0.996505	−	1.32103i
$679$	27.7449	+	48.0555i	1.06475	+	1.84420i
$680$		0			0
$681$	−0.913870	−	2.15594i	−0.0350196	−	0.0826157i
$682$	−10.8532	+	18.7984i	−0.415592	+	0.719827i
$683$	38.4610			1.47167			0.735834	−	0.677162i	$-0.236790\pi$
$683$	38.4610			1.47167			0.735834	+	0.677162i	$0.236790\pi$
$684$	−3.17968	+	3.28608i	−0.121578	+	0.125646i
$685$		0			0
$686$	11.4926	−	19.9057i	0.438789	−	0.760005i
$687$	14.1571	+	1.74545i	0.540127	+	0.0665932i
$688$	1.30114	+	2.25363i	0.0496054	+	0.0859190i
$689$	−1.35194	−	2.34163i	−0.0515048	−	0.0892089i
$690$		0			0
$691$	−0.240304	+	0.416219i	−0.00914159	+	0.0158337i	−0.870560	−	0.492062i	$-0.836243\pi$
$691$	−0.240304	+	0.416219i	−0.00914159	+	0.0158337i	0.861418	+	0.507896i	$0.169577\pi$
$692$	−54.2084			−2.06070
$693$	−11.5242	+	11.9098i	−0.437768	+	0.452417i
$694$	1.47841			0.0561197
$695$		0			0
$696$	1.92369	+	4.53824i	0.0729174	+	0.172021i
$697$	0.121457	+	0.210370i	0.00460053	+	0.00796835i
$698$	22.2637	+	38.5619i	0.842694	+	1.45959i
$699$	−8.95725	+	11.8743i	−0.338794	+	0.449128i
$700$		0			0
$701$	−18.1797			−0.686637			−0.343318	−	0.939219i	$-0.611551\pi$
$701$	−18.1797			−0.686637			−0.343318	+	0.939219i	$0.611551\pi$
$702$	6.55451	+	2.52732i	0.247384	+	0.0953875i
$703$	−4.87614			−0.183907
$704$	−7.11404	+	12.3219i	−0.268120	+	0.464398i
$705$		0			0
$706$	−10.5316	−	18.2413i	−0.396363	−	0.686520i
$707$	−3.00000	−	5.19615i	−0.112827	−	0.195421i
$708$	6.63322	+	15.6486i	0.249292	+	0.588111i
$709$	−3.59355	+	6.22421i	−0.134959	+	0.233755i	−0.925582	−	0.378548i	$-0.876423\pi$
$709$	−3.59355	+	6.22421i	−0.134959	+	0.233755i	0.790623	+	0.612303i	$0.209757\pi$
$710$		0			0
$711$	30.1042	+	7.53778i	1.12900	+	0.282689i
$712$	−2.20257			−0.0825449
$713$	−18.4331	+	31.9270i	−0.690323	+	1.19568i
$714$	19.8105	+	2.44247i	0.741389	+	0.0914071i
$715$		0			0
$716$	−2.62015	−	4.53824i	−0.0979197	−	0.169602i
$717$	41.1271	+	5.07063i	1.53592	+	0.189366i
$718$	−31.8737	+	55.2069i	−1.18952	+	2.06030i
$719$	12.5168			0.466797			0.233399	−	0.972381i	$-0.425015\pi$
$719$	12.5168			0.466797			0.233399	+	0.972381i	$0.425015\pi$
$720$		0			0
$721$	30.7449			1.14500
$722$	19.3802	−	33.5674i	0.721255	−	1.24925i
$723$	−4.21826	−	9.95141i	−0.156879	−	0.370097i
$724$	−0.550803	−	0.954019i	−0.0204704	−	0.0354558i
$725$		0			0
$726$	−19.9586	+	26.4584i	−0.740732	+	0.981963i
$727$	4.21292	−	7.29699i	0.156249	−	0.270631i	−0.777264	−	0.629174i	$-0.783393\pi$
$727$	4.21292	−	7.29699i	0.156249	−	0.270631i	0.933513	+	0.358544i	$0.116727\pi$
$728$	1.94418			0.0720562
$729$	20.0107	+	18.1266i	0.741136	+	0.671355i
$730$		0			0
$731$	−0.554512	+	0.960443i	−0.0205094	+	0.0355233i
$732$	−9.37211	+	12.4243i	−0.346403	+	0.459215i
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$	−7.48887	−	12.9711i	−0.276419	−	0.478772i
$735$		0			0
$736$	−19.3663	+	33.5434i	−0.713852	+	1.23643i
$737$	11.0074			0.405463
$738$	0.308874	+	1.08125i	0.0113698	+	0.0398013i
$739$	−1.81290			−0.0666887			−0.0333444	−	0.999444i	$-0.510616\pi$
$739$	−1.81290			−0.0666887			−0.0333444	+	0.999444i	$0.510616\pi$
$740$		0			0
$741$	0.721965	+	0.0890123i	0.0265220	+	0.00326995i
$742$	−17.7826	−	30.8003i	−0.652819	−	1.13072i
$743$	10.0686	+	17.4393i	0.369380	+	0.639785i	0.989469	−	0.144747i	$-0.0462367\pi$
$743$	10.0686	+	17.4393i	0.369380	+	0.639785i	−0.620089	+	0.784532i	$0.712903\pi$
$744$	9.71370	+	1.19762i	0.356122	+	0.0439068i
$745$		0			0
$746$	45.7374			1.67457
$747$	35.6739	+	8.93237i	1.30524	+	0.326818i
$748$	−4.29873			−0.157177
$749$	−2.47209	+	4.28179i	−0.0903282	+	0.156453i
$750$		0			0
$751$	−6.10662	−	10.5770i	−0.222834	−	0.385959i	0.732834	−	0.680408i	$-0.238197\pi$
$751$	−6.10662	−	10.5770i	−0.222834	−	0.385959i	−0.955667	+	0.294449i	$0.904864\pi$
$752$	−17.2991	−	29.9628i	−0.630832	−	1.09263i
$753$	−29.8031	+	39.5089i	−1.08608	+	1.43979i
$754$	2.62015	−	4.53824i	0.0954203	−	0.165273i
$755$		0			0
$756$	46.5931	+	17.9656i	1.69457	+	0.653402i
$757$	−52.9533			−1.92462			−0.962310	−	0.271955i	$-0.912330\pi$
$757$	−52.9533			−1.92462			−0.962310	+	0.271955i	$0.912330\pi$
$758$	18.1419	−	31.4228i	0.658945	−	1.14133i
$759$	6.75468	−	8.95445i	0.245179	−	0.325026i
$760$		0			0
$761$	9.22677	+	15.9812i	0.334470	+	0.579319i	0.983383	−	0.181543i	$-0.0581093\pi$
$761$	9.22677	+	15.9812i	0.334470	+	0.579319i	−0.648913	+	0.760863i	$0.724776\pi$
$762$	9.98212	+	23.5491i	0.361614	+	0.853094i
$763$	28.8158	−	49.9105i	1.04320	−	1.80688i
$764$	−47.5752			−1.72121
$765$		0			0
$766$	−0.992582			−0.0358634
$767$	1.35194	−	2.34163i	0.0488157	−	0.0845513i
$768$	−15.4458	−	1.90434i	−0.557353	−	0.0687169i
$769$	2.22677	+	3.85688i	0.0802995	+	0.139083i	0.903379	−	0.428844i	$-0.141079\pi$
$769$	2.22677	+	3.85688i	0.0802995	+	0.139083i	−0.823079	+	0.567927i	$0.807746\pi$
$770$		0			0
$771$	−30.9426	−	3.81497i	−1.11437	−	0.137393i
$772$	−23.4363	+	40.5929i	−0.843491	+	1.46097i
$773$	−38.9368			−1.40046			−0.700229	−	0.713918i	$-0.746919\pi$
$773$	−38.9368			−1.40046			−0.700229	+	0.713918i	$0.746919\pi$
$774$	−3.56999	+	3.68945i	−0.128321	+	0.132614i
$775$		0			0
$776$	−4.98516	+	8.63456i	−0.178957	+	0.309962i
$777$	20.7826	+	49.0288i	0.745571	+	1.75890i
$778$	5.82806	+	10.0945i	0.208946	+	0.361905i
$779$	0.0582214	+	0.100842i	0.00208600	+	0.00361305i
$780$		0			0
$781$	−4.13453	+	7.16121i	−0.147945	+	0.256248i
$782$	−13.5094			−0.483094
$783$	15.6715	−	12.6517i	0.560053	−	0.452134i
$784$	−30.7597			−1.09856
$785$		0			0
$786$	−13.0558	+	17.3077i	−0.465686	+	0.617344i
$787$	17.1140	+	29.6424i	0.610050	+	1.05664i	0.991231	+	0.132137i	$0.0421838\pi$
$787$	17.1140	+	29.6424i	0.610050	+	1.05664i	−0.381182	+	0.924500i	$0.624483\pi$
$788$	−18.3216	−	31.7340i	−0.652681	−	1.13048i
$789$	−21.5423	−	50.8210i	−0.766926	−	1.80928i
$790$		0			0
$791$	−48.7252			−1.73247
$792$	−2.88857	−	0.723268i	−0.102641	−	0.0257002i
$793$	2.47580			0.0879183
$794$	3.91387	−	6.77902i	0.138898	−	0.240578i
$795$		0			0
$796$	−4.21564	−	7.30171i	−0.149420	−	0.258802i
$797$	11.9828	+	20.7547i	0.424451	+	0.735171i	0.996369	−	0.0851400i	$-0.0271337\pi$
$797$	11.9828	+	20.7547i	0.424451	+	0.735171i	−0.571918	+	0.820311i	$0.693800\pi$
$798$	9.49629	+	1.17081i	0.336165	+	0.0414464i
$799$	7.37243	−	12.7694i	0.260818	−	0.451750i
$800$		0			0
$801$	2.47209	+	8.65383i	0.0873470	+	0.305768i
$802$	49.1600			1.73590
$803$	8.34452	−	14.4531i	0.294472	−	0.510040i
$804$	−12.9444	−	30.5375i	−0.456513	−	1.07697i
$805$		0			0
$806$	−5.20257	−	9.01112i	−0.183253	−	0.317403i
$807$	−32.8536	+	43.5529i	−1.15650	+	1.53313i
$808$	0.539036	−	0.933638i	0.0189632	−	0.0328453i
$809$	−0.283896			−0.00998124			−0.00499062	−	0.999988i	$-0.501589\pi$
$809$	−0.283896			−0.00998124			−0.00499062	+	0.999988i	$0.501589\pi$
$810$		0			0
$811$	32.4413			1.13917			0.569584	−	0.821933i	$-0.307104\pi$
$811$	32.4413			1.13917			0.569584	+	0.821933i	$0.307104\pi$
$812$	18.6255	−	32.2603i	0.653626	−	1.13211i
$813$	−3.37985	+	4.48055i	−0.118536	+	0.157140i
$814$	−10.6103	−	18.3776i	−0.371892	−	0.644136i
$815$		0			0
$816$	−2.89903	−	6.83919i	−0.101486	−	0.239420i
$817$	−0.265809	+	0.460395i	−0.00929948	+	0.0161072i
$818$	2.18710			0.0764701
$819$	−2.18208	−	7.63862i	−0.0762481	−	0.266915i
$820$		0			0
$821$	−20.8347	+	36.0868i	−0.727136	+	1.25944i	0.230953	+	0.972965i	$0.425816\pi$
$821$	−20.8347	+	36.0868i	−0.727136	+	1.25944i	−0.958089	+	0.286472i	$0.907518\pi$
$822$	−26.7826	−	3.30207i	−0.934150	−	0.115173i
$823$	−9.68130	−	16.7685i	−0.337469	−	0.584514i	0.646487	−	0.762925i	$-0.276237\pi$
$823$	−9.68130	−	16.7685i	−0.337469	−	0.584514i	−0.983956	+	0.178412i	$0.942904\pi$
$824$	2.76210	+	4.78410i	0.0962223	+	0.166662i
$825$		0			0
$826$	17.7826	−	30.8003i	0.618735	−	1.07168i
$827$	−18.8097			−0.654076			−0.327038	−	0.945011i	$-0.606050\pi$
$827$	−18.8097			−0.654076			−0.327038	+	0.945011i	$0.606050\pi$
$828$	−32.7853	−	8.20910i	−1.13937	−	0.285286i
$829$	−33.1016			−1.14967			−0.574833	−	0.818271i	$-0.694933\pi$
$829$	−33.1016			−1.14967			−0.574833	+	0.818271i	$0.694933\pi$
$830$		0			0
$831$	3.77517	+	8.90611i	0.130959	+	0.308950i
$832$	−3.41016	−	5.90657i	−0.118226	−	0.204774i
$833$	−6.55451	−	11.3527i	−0.227100	−	0.393349i
$834$	17.4078	−	23.0769i	0.602781	−	0.799087i
$835$		0			0
$836$	−2.06063			−0.0712682
$837$	−6.19692	−	39.5089i	−0.214197	−	1.36563i
$838$	−54.0719			−1.86788
$839$	19.8482	−	34.3781i	0.685237	−	1.18687i	−0.288125	−	0.957593i	$-0.593032\pi$
$839$	19.8482	−	34.3781i	0.685237	−	1.18687i	0.973362	−	0.229273i	$-0.0736347\pi$
$840$		0			0
$841$	6.98777	+	12.1032i	0.240958	+	0.417351i
$842$	−7.96969	−	13.8039i	−0.274654	−	0.475714i
$843$	−16.2937	−	38.4390i	−0.561185	−	1.32391i
$844$	−17.6308	+	30.5375i	−0.606878	+	1.05114i
$845$		0			0
$846$	47.4642	−	49.0525i	1.63185	−	1.68646i
$847$	37.4791			1.28780
$848$	−6.61775	+	11.4623i	−0.227254	+	0.393616i
$849$	−18.1226	−	2.23436i	−0.621965	−	0.0766831i
$850$		0			0
$851$	−18.0205	−	31.2124i	−0.617734	−	1.06995i
$852$	24.7292	+	3.04890i	0.847208	+	0.104454i
$853$	−2.05822	+	3.56494i	−0.0704722	+	0.122061i	−0.899108	−	0.437726i	$-0.855784\pi$
$853$	−2.05822	+	3.56494i	−0.0704722	+	0.122061i	0.828636	+	0.559788i	$0.189117\pi$
$854$	32.5652			1.11436
$855$		0			0
$856$	−0.888365			−0.0303637
$857$	7.37243	−	12.7694i	0.251837	−	0.436195i	−0.712194	−	0.701982i	$-0.752299\pi$
$857$	7.37243	−	12.7694i	0.251837	−	0.436195i	0.964032	+	0.265787i	$0.0856319\pi$
$858$	1.23550	+	2.91469i	0.0421792	+	0.0995060i
$859$	18.9269	+	32.7824i	0.645779	+	1.11852i	0.984121	+	0.177499i	$0.0568006\pi$
$859$	18.9269	+	32.7824i	0.645779	+	1.11852i	−0.338342	+	0.941023i	$0.609866\pi$
$860$		0			0
$861$	0.765809	−	1.01521i	0.0260987	−	0.0345982i
$862$	−8.32905	+	14.4263i	−0.283688	+	0.491363i
$863$	−26.7704			−0.911274			−0.455637	−	0.890166i	$-0.650588\pi$
$863$	−26.7704			−0.911274			−0.455637	+	0.890166i	$0.650588\pi$
$864$	−6.51067	−	41.5093i	−0.221497	−	1.41217i
$865$		0			0
$866$	−13.0508	+	22.6047i	−0.443484	+	0.768137i
$867$	−15.8257	+	20.9795i	−0.537467	+	0.712503i
$868$	−36.9828	−	64.0560i	−1.25528	−	2.17420i
$869$	6.99258	+	12.1115i	0.237207	+	0.410855i
$870$		0			0
$871$	−2.63824	+	4.56956i	−0.0893933	+	0.154834i
$872$	10.3552			0.350671
$873$	39.5200	+	9.89540i	1.33755	+	0.334909i
$874$	−6.47580			−0.219047
$875$		0			0
$876$	−49.9097	−	6.15345i	−1.68629	−	0.207906i
$877$	−23.4841	−	40.6756i	−0.793001	−	1.37352i	−0.924101	−	0.382148i	$-0.875184\pi$
$877$	−23.4841	−	40.6756i	−0.793001	−	1.37352i	0.131101	−	0.991369i	$-0.458149\pi$
$878$	9.14195	+	15.8343i	0.308526	+	0.534382i
$879$	32.6489	+	4.02534i	1.10122	+	0.135771i
$880$		0			0
$881$	−19.8055			−0.667264			−0.333632	−	0.942703i	$-0.608274\pi$
$881$	−19.8055			−0.667264			−0.333632	+	0.942703i	$0.608274\pi$
$882$	−16.6686	−	58.3501i	−0.561259	−	1.96475i
$883$	6.20257			0.208733			0.104367	−	0.994539i	$-0.466718\pi$
$883$	6.20257			0.208733			0.104367	+	0.994539i	$0.466718\pi$
$884$	1.03031	−	1.78455i	0.0346532	−	0.0600210i
$885$		0			0
$886$	3.82905	+	6.63210i	0.128639	+	0.222810i
$887$	6.71370	+	11.6285i	0.225424	+	0.390446i	0.956447	−	0.291907i	$-0.0942899\pi$
$887$	6.71370	+	11.6285i	0.225424	+	0.390446i	−0.731023	+	0.682353i	$0.760957\pi$
$888$	−5.76210	+	7.63862i	−0.193363	+	0.256335i
$889$	14.4623	−	25.0494i	0.485049	−	0.840129i
$890$		0			0
$891$	0.400338	+	12.1609i	0.0134118	+	0.407404i
$892$	63.1049			2.11291
$893$	3.53402	−	6.12111i	0.118262	−	0.204835i
$894$	−23.0323	+	30.5331i	−0.770314	+	1.02118i
$895$		0			0
$896$	−11.8142	−	20.4628i	−0.394685	−	0.683614i
$897$	2.09836	+	4.95029i	0.0700621	+	0.165285i
$898$	−29.3855	+	50.8972i	−0.980607	+	1.69846i
$899$	−29.8325			−0.994971
$900$		0			0
$901$	−5.64064			−0.187917
$902$	−0.253376	+	0.438860i	−0.00843650	+	0.0146124i
$903$	5.76210	+	0.710419i	0.191751	+	0.0236413i
$904$	−4.37744	−	7.58196i	−0.145592	−	0.252172i
$905$		0			0
$906$	−63.4618	−	7.82431i	−2.10838	−	0.259945i
$907$	0.336783	−	0.583325i	0.0111827	−	0.0193690i	−0.860380	−	0.509653i	$-0.829774\pi$
$907$	0.336783	−	0.583325i	0.0111827	−	0.0193690i	0.871563	+	0.490284i	$0.163107\pi$
$908$	−3.17968			−0.105521
$909$	−4.27323	−	1.06997i	−0.141734	−	0.0354887i
$910$		0			0
$911$	3.95485	−	6.85000i	0.131030	−	0.226951i	−0.793044	−	0.609165i	$-0.791505\pi$
$911$	3.95485	−	6.85000i	0.131030	−	0.226951i	0.924074	+	0.382214i	$0.124838\pi$
$912$	−1.38967	−	3.27841i	−0.0460166	−	0.108559i
$913$	8.28630	+	14.3523i	0.274236	+	0.474992i
$914$	36.7802	+	63.7052i	1.21658	+	2.10718i
$915$		0			0
$916$	9.68469	−	16.7744i	0.319991	−	0.554241i
$917$	24.5168			0.809615
$918$	11.4027	−	9.20550i	0.376347	−	0.303827i
$919$	−8.58263			−0.283115			−0.141557	−	0.989930i	$-0.545211\pi$
$919$	−8.58263			−0.283115			−0.141557	+	0.989930i	$0.545211\pi$
$920$		0			0
$921$	−30.7486	+	40.7623i	−1.01320	+	1.34316i
$922$	−36.1702	−	62.6486i	−1.19120	−	2.06322i
$923$	−1.98191	−	3.43277i	−0.0652355	−	0.112991i
$924$	8.78259	+	20.7193i	0.288926	+	0.681614i
$925$		0			0
$926$	−15.5390			−0.510644
$927$	15.6965	−	16.2217i	0.515539	−	0.532790i
$928$	−31.3430			−1.02888
$929$	−14.8081	+	25.6484i	−0.485838	+	0.841496i	−0.999868	−	0.0162766i	$-0.994819\pi$
$929$	−14.8081	+	25.6484i	−0.485838	+	0.841496i	0.514030	+	0.857772i	$0.328152\pi$
$930$		0			0
$931$	−3.14195	−	5.44201i	−0.102973	−	0.178355i
$932$	10.0986	+	17.4912i	0.330789	+	0.572944i
$933$	16.1805	+	1.99492i	0.529727	+	0.0653109i
$934$	31.2560	−	54.1370i	1.02273	−	1.77142i
$935$		0			0
$936$	0.992582	−	1.02580i	0.0324435	−	0.0335292i
$937$	15.2058			0.496753			0.248376	−	0.968664i	$-0.420103\pi$
$937$	15.2058			0.496753			0.248376	+	0.968664i	$0.420103\pi$
$938$	−34.7018	+	60.1053i	−1.13305	+	1.96251i
$939$	−7.85544	−	18.5320i	−0.256353	−	0.604769i
$940$		0			0
$941$	−2.82643	−	4.89553i	−0.0921391	−	0.159590i	0.816272	−	0.577668i	$-0.196037\pi$
$941$	−2.82643	−	4.89553i	−0.0921391	−	0.159590i	−0.908411	+	0.418078i	$0.862704\pi$
$942$	5.50872	−	7.30273i	0.179484	−	0.237936i
$943$	−0.430332	+	0.745356i	−0.0140135	+	0.0242721i
$944$	−13.2355			−0.430779
$945$		0			0
$946$	−2.31357			−0.0752206
$947$	−20.1981	+	34.9841i	−0.656350	+	1.13683i	0.325204	+	0.945644i	$0.394567\pi$
$947$	−20.1981	+	34.9841i	−0.656350	+	1.13683i	−0.981554	+	0.191187i	$0.938766\pi$
$948$	25.3774	−	33.6420i	0.824221	−	1.09264i
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$		0			0
$951$	6.20518	+	14.6388i	0.201217	+	0.474696i
$952$	2.02791	−	3.51244i	0.0657249	−	0.113839i
$953$	22.9320			0.742839			0.371419	−	0.928465i	$-0.378871\pi$
$953$	22.9320			0.742839			0.371419	+	0.928465i	$0.378871\pi$
$954$	−25.3297	−	6.34229i	−0.820079	−	0.205339i
$955$		0			0
$956$	28.1345	−	48.7304i	0.909936	−	1.57605i
$957$	9.00826	+	1.11064i	0.291196	+	0.0359020i
$958$	8.32905	+	14.4263i	0.269099	+	0.466094i
$959$	15.2584	+	26.4283i	0.492719	+	0.853415i
$960$		0			0
$961$	−14.1177	+	24.4527i	−0.455411	+	0.788795i
$962$	10.1723			0.327967
$963$	0.997070	+	3.49035i	0.0321301	+	0.112475i
$964$	−14.6768			−0.472708
$965$		0			0
$966$	27.6005	+	65.1131i	0.888032	+	2.09498i
$967$	5.18501	+	8.98071i	0.166739	+	0.288800i	0.937271	−	0.348601i	$-0.113343\pi$
$967$	5.18501	+	8.98071i	0.166739	+	0.288800i	−0.770533	+	0.637401i	$0.780010\pi$
$968$	3.36710	+	5.83198i	0.108223	+	0.187447i
$969$	0.913870	−	1.21149i	0.0293577	−	0.0389186i
$970$		0			0
$971$	48.0410			1.54171			0.770854	−	0.637012i	$-0.219830\pi$
$971$	48.0410			1.54171			0.770854	+	0.637012i	$0.219830\pi$
$972$	33.2667	−	15.4115i	1.06703	−	0.494323i
$973$	−32.6890			−1.04796
$974$	−12.4586	+	21.5789i	−0.399198	+	0.691431i
$975$		0			0
$976$	−6.05953	−	10.4954i	−0.193961	−	0.335950i
$977$	13.5266	+	23.4288i	0.432754	+	0.749553i	0.997109	−	0.0759796i	$-0.0242084\pi$
$977$	13.5266	+	23.4288i	0.432754	+	0.749553i	−0.564355	+	0.825532i	$0.690875\pi$
$978$	−11.9522	−	28.1969i	−0.382190	−	0.901636i
$979$	−2.02791	+	3.51244i	−0.0648122	+	0.112258i
$980$		0			0
$981$	−11.6223	−	40.6852i	−0.371072	−	1.29898i
$982$	−19.2355			−0.613829
$983$	−11.2408	+	19.4697i	−0.358527	+	0.620987i	−0.987715	−	0.156266i	$-0.950054\pi$
$983$	−11.2408	+	19.4697i	−0.358527	+	0.620987i	0.629188	+	0.777253i	$0.283388\pi$
$984$	0.226773	+	0.0279592i	0.00722925	+	0.000891306i
$985$		0			0
$986$	−5.46598	−	9.46735i	−0.174072	−	0.301502i
$987$	−76.6091	−	9.44526i	−2.43849	−	0.300646i
$988$	0.493887	−	0.855437i	0.0157126	−	0.0272151i
$989$	−3.92935			−0.124946
$990$		0			0
$991$	−26.5316			−0.842805			−0.421402	−	0.906874i	$-0.638462\pi$
$991$	−26.5316			−0.842805			−0.421402	+	0.906874i	$0.638462\pi$
$992$	−31.1173	+	53.8967i	−0.987975	+	1.71122i
$993$	−4.88095	−	11.5148i	−0.154892	−	0.365410i
$994$	−26.0689	−	45.1526i	−0.826855	−	1.43215i
$995$		0			0
$996$	30.0726	−	39.8662i	0.952887	−	1.26321i
$997$	−14.1829	+	24.5656i	−0.449178	+	0.777999i	−0.998333	−	0.0577217i	$-0.981616\pi$
$997$	−14.1829	+	24.5656i	−0.449178	+	0.777999i	0.549155	+	0.835721i	$0.314950\pi$
$998$	62.9433			1.99243
$999$	36.4791	+	14.0658i	1.15415	+	0.445021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.e.b.151.1		6
3.2	odd	2		675.2.e.b.451.3		6
5.2	odd	4		225.2.k.b.124.2		12
5.3	odd	4		225.2.k.b.124.5		12
5.4	even	2		45.2.e.b.16.3	✓	6
9.2	odd	6		2025.2.a.o.1.1		3
9.4	even	3	inner	225.2.e.b.76.1		6
9.5	odd	6		675.2.e.b.226.3		6
9.7	even	3		2025.2.a.n.1.3		3
15.2	even	4		675.2.k.b.424.5		12
15.8	even	4		675.2.k.b.424.2		12
15.14	odd	2		135.2.e.b.46.1		6
20.19	odd	2		720.2.q.i.241.3		6
45.2	even	12		2025.2.b.m.649.2		6
45.4	even	6		45.2.e.b.31.3	yes	6
45.7	odd	12		2025.2.b.l.649.5		6
45.13	odd	12		225.2.k.b.49.2		12
45.14	odd	6		135.2.e.b.91.1		6
45.22	odd	12		225.2.k.b.49.5		12
45.23	even	12		675.2.k.b.199.5		12
45.29	odd	6		405.2.a.i.1.3		3
45.32	even	12		675.2.k.b.199.2		12
45.34	even	6		405.2.a.j.1.1		3
45.38	even	12		2025.2.b.m.649.5		6
45.43	odd	12		2025.2.b.l.649.2		6
60.59	even	2		2160.2.q.k.721.3		6
180.59	even	6		2160.2.q.k.1441.3		6
180.79	odd	6		6480.2.a.bv.1.1		3
180.119	even	6		6480.2.a.bs.1.1		3
180.139	odd	6		720.2.q.i.481.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.3	✓	6	5.4	even	2
45.2.e.b.31.3	yes	6	45.4	even	6
135.2.e.b.46.1		6	15.14	odd	2
135.2.e.b.91.1		6	45.14	odd	6
225.2.e.b.76.1		6	9.4	even	3	inner
225.2.e.b.151.1		6	1.1	even	1	trivial
225.2.k.b.49.2		12	45.13	odd	12
225.2.k.b.49.5		12	45.22	odd	12
225.2.k.b.124.2		12	5.2	odd	4
225.2.k.b.124.5		12	5.3	odd	4
405.2.a.i.1.3		3	45.29	odd	6
405.2.a.j.1.1		3	45.34	even	6
675.2.e.b.226.3		6	9.5	odd	6
675.2.e.b.451.3		6	3.2	odd	2
675.2.k.b.199.2		12	45.32	even	12
675.2.k.b.199.5		12	45.23	even	12
675.2.k.b.424.2		12	15.8	even	4
675.2.k.b.424.5		12	15.2	even	4
720.2.q.i.241.3		6	20.19	odd	2
720.2.q.i.481.3		6	180.139	odd	6
2025.2.a.n.1.3		3	9.7	even	3
2025.2.a.o.1.1		3	9.2	odd	6
2025.2.b.l.649.2		6	45.43	odd	12
2025.2.b.l.649.5		6	45.7	odd	12
2025.2.b.m.649.2		6	45.2	even	12
2025.2.b.m.649.5		6	45.38	even	12
2160.2.q.k.721.3		6	60.59	even	2
2160.2.q.k.1441.3		6	180.59	even	6
6480.2.a.bs.1.1		3	180.119	even	6
6480.2.a.bv.1.1		3	180.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04307 + 1.80664i) q^{2} +(1.04307 - 1.38276i) q^{3} +(-1.17597 - 2.03684i) q^{4} +(1.41016 + 3.32675i) q^{6} +(2.04307 - 3.53869i) q^{7} +0.734191 q^{8} +(-0.824030 - 2.88461i) q^{9} +O(q^{10})\)	\(q+(-1.04307 + 1.80664i) q^{2} +(1.04307 - 1.38276i) q^{3} +(-1.17597 - 2.03684i) q^{4} +(1.41016 + 3.32675i) q^{6} +(2.04307 - 3.53869i) q^{7} +0.734191 q^{8} +(-0.824030 - 2.88461i) q^{9} +(0.675970 - 1.17081i) q^{11} +(-4.04307 - 0.498476i) q^{12} +(0.324030 + 0.561237i) q^{13} +(4.26210 + 7.38217i) q^{14} +(1.58613 - 2.74726i) q^{16} +1.35194 q^{17} +(6.07097 + 1.52011i) q^{18} +0.648061 q^{19} +(-2.76210 - 6.51615i) q^{21} +(1.41016 + 2.44247i) q^{22} +(2.39500 + 4.14827i) q^{23} +(0.765809 - 1.01521i) q^{24} -1.35194 q^{26} +(-4.84823 - 1.86940i) q^{27} -9.61033 q^{28} +(-1.93807 + 3.35683i) q^{29} +(3.84823 + 6.66533i) q^{31} +(4.04307 + 7.00279i) q^{32} +(-0.913870 - 2.15594i) q^{33} +(-1.41016 + 2.44247i) q^{34} +(-4.90645 + 5.07063i) q^{36} -7.52420 q^{37} +(-0.675970 + 1.17081i) q^{38} +(1.11404 + 0.137352i) q^{39} +(0.0898394 + 0.155606i) q^{41} +(14.6534 + 1.80664i) q^{42} +(-0.410161 + 0.710419i) q^{43} -3.17968 q^{44} -9.99258 q^{46} +(5.45323 - 9.44526i) q^{47} +(-2.14435 - 5.05880i) q^{48} +(-4.84823 - 8.39738i) q^{49} +(1.41016 - 1.86940i) q^{51} +(0.762100 - 1.32000i) q^{52} -4.17226 q^{53} +(8.43436 - 6.80911i) q^{54} +(1.50000 - 2.59808i) q^{56} +(0.675970 - 0.896110i) q^{57} +(-4.04307 - 7.00279i) q^{58} +(-2.08613 - 3.61328i) q^{59} +(1.91016 - 3.30850i) q^{61} -16.0558 q^{62} +(-11.8913 - 2.97746i) q^{63} -10.5242 q^{64} +(4.84823 + 0.597746i) q^{66} +(4.07097 + 7.05113i) q^{67} +(-1.58984 - 2.75368i) q^{68} +(8.23419 + 1.01521i) q^{69} -6.11644 q^{71} +(-0.604996 - 2.11785i) q^{72} +12.3445 q^{73} +(7.84823 - 13.5935i) q^{74} +(-0.762100 - 1.32000i) q^{76} +(-2.76210 - 4.78410i) q^{77} +(-1.41016 + 1.86940i) q^{78} +(-5.17226 + 8.95862i) q^{79} +(-7.64195 + 4.75401i) q^{81} -0.374833 q^{82} +(-6.12920 + 10.6161i) q^{83} +(-10.0242 + 13.2887i) q^{84} +(-0.855648 - 1.48203i) q^{86} +(2.62015 + 6.18127i) q^{87} +(0.496291 - 0.859601i) q^{88} -3.00000 q^{89} +2.64806 q^{91} +(5.63290 - 9.75648i) q^{92} +(13.2305 + 1.63121i) q^{93} +(11.3761 + 19.7041i) q^{94} +(13.9003 + 1.71380i) q^{96} +(-6.79001 + 11.7606i) q^{97} +20.2281 q^{98} +(-3.93436 - 0.985122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q + q^2 - q^3 - 5 * q^4 - 4 * q^6 + 5 * q^7 - 6 * q^8 - 7 * q^9	\( 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9} + 2 q^{11} - 17 q^{12} + 4 q^{13} + 9 q^{14} - 5 q^{16} + 4 q^{17} + 23 q^{18} + 8 q^{19} - 4 q^{22} + 3 q^{23} + 15 q^{24} - 4 q^{26} + 2 q^{27} - 10 q^{28} + 7 q^{29} - 8 q^{31} + 17 q^{32} - 20 q^{33} + 4 q^{34} + 10 q^{36} - 12 q^{37} - 2 q^{38} - 14 q^{39} + 13 q^{41} + 33 q^{42} + 10 q^{43} - 44 q^{44} - 6 q^{46} + 13 q^{47} + 10 q^{48} + 2 q^{49} - 4 q^{51} - 12 q^{52} + 4 q^{53} + 5 q^{54} + 9 q^{56} + 2 q^{57} - 17 q^{58} + 2 q^{59} - q^{61} - 84 q^{62} - 33 q^{63} - 30 q^{64} - 2 q^{66} + 11 q^{67} - 22 q^{68} + 39 q^{69} - 20 q^{71} - 15 q^{72} + 16 q^{73} + 16 q^{74} + 12 q^{76} + 4 q^{78} - 2 q^{79} - 19 q^{81} + 58 q^{82} - 15 q^{83} - 27 q^{84} - 28 q^{86} + 26 q^{87} - 24 q^{88} - 18 q^{89} + 20 q^{91} + 39 q^{92} + 42 q^{93} + 31 q^{94} + 13 q^{96} - 18 q^{97} + 80 q^{98} + 22 q^{99}+O(q^{100}) \) 6 * q + q^2 - q^3 - 5 * q^4 - 4 * q^6 + 5 * q^7 - 6 * q^8 - 7 * q^9 + 2 * q^11 - 17 * q^12 + 4 * q^13 + 9 * q^14 - 5 * q^16 + 4 * q^17 + 23 * q^18 + 8 * q^19 - 4 * q^22 + 3 * q^23 + 15 * q^24 - 4 * q^26 + 2 * q^27 - 10 * q^28 + 7 * q^29 - 8 * q^31 + 17 * q^32 - 20 * q^33 + 4 * q^34 + 10 * q^36 - 12 * q^37 - 2 * q^38 - 14 * q^39 + 13 * q^41 + 33 * q^42 + 10 * q^43 - 44 * q^44 - 6 * q^46 + 13 * q^47 + 10 * q^48 + 2 * q^49 - 4 * q^51 - 12 * q^52 + 4 * q^53 + 5 * q^54 + 9 * q^56 + 2 * q^57 - 17 * q^58 + 2 * q^59 - q^61 - 84 * q^62 - 33 * q^63 - 30 * q^64 - 2 * q^66 + 11 * q^67 - 22 * q^68 + 39 * q^69 - 20 * q^71 - 15 * q^72 + 16 * q^73 + 16 * q^74 + 12 * q^76 + 4 * q^78 - 2 * q^79 - 19 * q^81 + 58 * q^82 - 15 * q^83 - 27 * q^84 - 28 * q^86 + 26 * q^87 - 24 * q^88 - 18 * q^89 + 20 * q^91 + 39 * q^92 + 42 * q^93 + 31 * q^94 + 13 * q^96 - 18 * q^97 + 80 * q^98 + 22 * q^99

Introduction

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